When did "cultural appropriation" become a concept?

18 March 1909 the US territory of New Mexico passed the Act for the Protection of the Industries of the Indians in New Mexico:

It shall be unlawful to sell or offer for sale within the Territory of New Mexico any imitation Indian blanket, unless manufactured in New Mexico and, unless the said imitation blanket shall have a label attached thereto on which shall be printed in letters not less than one and one-half inches square the words “Imitation Indian Blanket” stating which tribe it is designed to imitate. This label must be at all times maintained upon any imitation Indian blanket which is to be sold or offered for sale within the Territory. It shall also be unlawful to sell or offer for sale any imitation Indian baskets or pottery under representations that the imitations were manufactured by Indians, unless they should be manufactured by Indians. Any person violating this section shall be deemed guilty of a misdemeanor and shall be punished by a fine of not less than twenty-five dollars nor more than one hundred dollar for each offense, or by imprisonment in the county jail for not less than thirty days nor more than ninety days.

As far as the exact term "cultural appropriation" in the sense of the OP, this was in use at least by January 1964, when Harold Cruse published "Rebellion or Revolution" (part 4 of 4) in Liberator volume IV at page 15:

But in terms of the creative and artistic use of Negro cultural ingredients and the economic benefits derived therefrom, it was the Whites who reaped, by the simple practice of cultural appropriation of aesthetic ideas not native to their own tradition.

Short answer: The word formation can be found earlier. But "Cultural Appropriation" in its present meaning was conceptualised in academia in the 1970s,and was established or widespread by the 1980s. The main fields of study where it took hold and was used were sociology, anthropology, cultural studies and the like. The negative aspects it describes were part and parcel from the start, as most read the words not as "taking" and "adapting" or "appreciation" but as "taking away", "exploiting" and "expropriation", connotating a certain sense of misuse or abuse. When this academic and descriptive concept penetrated public discourse in a now almost dominant seeming fashion as prescriptive norms is not within the scope of this answer.

Long version:

According to Hans Peter Hahn: "Antinomien kultureller Aneignung: Einführung", Zeitschrift für Ethnologie, January 2011:

„Kulturelle Aneignung" ist ein relativ junger Begriff in der Ethnologie. Verwendungen sind in den Cultural studies ab den 1970er und in den Media studies ab den 1980er Jahren fest zustellen; dort wie im gegenwärtigen ethnologischen Gebrauch steht die Differenz zwischen verschiedenen Möglichkeiten der Wahrnehmung kultureller Phänomene im Vordergrund.

"Cultural appropriation" is a relatively recent term in ethnology. Usage examples are to be found in cultural studies from the 1970s and in media studies from the 1980s; there, as in the current ethnological use, the difference between different ways of perceiving cultural phenomena is dominating.

Now I do not want to say what some might do anyway: that post-colonial critical whiteness and related "fields of study" often did take a turn into the idiocy department on that, but it seems necessary to emphasise that:

Cultural appropriation is often mentioned but undertheorized in critical rhetorical and media studies.
_{Richard A. Rogers: "From Cultural Exchange to Transculturation: A Review and Reconceptualization of Cultural Appropriation", Communication Theory, Volume 16, Issue 4, 1 November 2006, Pages 474–503.}

It has to be differentiated between a company exploiting some aspects of some native culture and turning that into profit, often at the cost of precisely these natives –– or a white man wearing rastas or a certain style of clothing.

During the last ten years, the term appropriation has become ubiquitous in the discourse of many disciplines, but—despite its manifest usefulness in academic argument—it remains conceptually unstable.
Based on the range of literature addressing the topic, I identified four categories of cultural appropriation (adapted from Wallis & Malm, 1984; additional influences from Bakhtin, 1975/1981; Clifford, 1988; Goodwin & Gore, 1990; Ziff & Rao, 1997).

Based on the assumptions identified above, these four categories can best be understood as naming the conditions (historical, social, political, cultural, and economic) under which acts of appropriation occur. After briefly defining each of the four types of appropriation, I discuss, illustrate, and evaluate each in depth.

1. Cultural exchange: the reciprocal exchange of symbols, artifacts, rituals, genres, and/or technologies between cultures with roughly equal levels of power.
2. Cultural dominance: the use of elements of a dominant culture by members of a subordinated culture in a context in which the dominant culture has been imposed onto the subordinated culture, including appropriations that enact resistance.
3. Cultural exploitation: the appropriation of elements of a subordinated culture by a dominant culture without substantive reciprocity, permission, and/or compensation.
4. Transculturation: cultural elements created from and/or by multiple cultures, such that identification of a single originating culture is problematic, for example, multiple cultural appropriations structured in the dynamics of globalization and transnational capitalism creating hybrid forms.

Because of its associations with power, the term appropriation had a negative charge when it was first popularized within cultural studies. Drawing on Foucault’s notion of social discourse as a system of regulation, theorists analyzed the production of cultural meanings that occurred through the appropriation of an “other.” Edward Said’s Orientalism (1978) is the classic locus for such a description; it emphasizes the way the West used representations of “the Orient” to fulfill its own desires and consolidate its own power.

_{Kathleen Ashley & Véronique Plesch: "The Cultural Processes of 'Appropriation'", Journal of Medieval and Early Modern Studies 32:1, 2002.}

To illustrate this general assessment:

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If you expand the search up to 2018, it seems that Google book n-gram viewer suffers in its usefulness here from anti-anti-social mob media bias by excluding Twitter, Facebook, etc.

Two of the earliest papers using this concept reveal some of the transformative developments this concepts has undergone:

_{Nicholas Garnham & Raymond Williams: "Pierre Bourdieu and the sociology of culture: an introduction", Media, Culture and Society, Vol 2, Issue 3, 1980, pp. 209 - 223:}

The work of which La Distinction is a summation is thus a frontal assault upon all essentialist theories of cultural appropriation (taste) and cultural production (creativity), upon all notions of absolute, universal cultural values and especially upon the intelligentsia and the ideologies of intellectual and cultural autonomy from economic and political determinants which that intelligentsia has constructed in defence of its material and symbolic interests as ’the dominated fraction of the dominant class’.

And

_{Nadine Gordimer: "From Apartheid to Afrocentrism", English in Africa Vol. 7, No. 1 (Mar., 1980), pp. 45-50:}

Whites have not succeeded in any comparable act of appropriation of a black cultural tool or in fact in any real appropriation of black culture. But if writing by whites dealing with African experience at their level is not African literature because they are not an indigenous people and do not live the life of the masses, then one could say that black literature is not African culture because the art-form itself is

Even earlier origins seem to lie in philosophy (Bernard J. F. Lonergan: "Appropriation of truth", in Malcolm Theodore Carron (ed.): "Readings in the Philosophy of Education, University of Detroit Press: Detroit, 1963).

It seems to be the case that if the words were used in this exact formation prior to that, their meaning was either not defined at all, just used en passant (assuming an immediate understanding, based on its Latin etymology), sometimes even in the exact opposite way of how they are commonly understood today (like acculturation or assimilation). Sometimes their meanings were at least completely different: Like in the context of agri-culture appropriation (compare that also to the hits where your search engine indexes linebreak hyphens as separate words.) Example: Martin L. Fausold, New York History; Cooperstown, N.Y., etc. Bd. 51, Ausg. 1, (Jan 1, 1970): 43. "James W. Wadsworth Sr. and The Meat Inspection Act of 1906"

A nice summary is found here:

The concept of cultural appropriation emerged in academia in the late 1970s and 1980s as part of the scholarly critique of colonialism. By the mid-1990s, it had gained a solid place in academic discourse, particularly in the field of sociology.

Some of this critique was rightly directed at literal cultural theft — the pilfering of art and artifacts by colonial powers — or glaring injustices, such as white entertainers in the pre-civil rights years profiting off black musical styles while black performers’ careers were hobbled by racism. Critics such as Edward Said offered valuable insight into Orientalism, the West’s tendency to fetishize Asians as exotic stereotypes.

But the hunt for wrongdoing has gone run amok. The recent anti-appropriation rhetoric has targeted creative products from art to literature to clothing. Nothing is too petty for the new culture cops: I have seen them rebuke a Filipina woman who purchased a bracelet with a yin-yang symbol at a fair and earnestly discuss whether it’s appropriation to eat Japanese, Indian or Thai food. Even Selena Gomez, a Latina artist, was assailed a couple of years ago for sporting a Hindu forehead dot, or bindi, in a Bollywood-style performance.

In some social-justice quarters, the demonization of “appropriative” interests converges with ultra-reactionary ideas about racial and cultural purity. I once read an anguished blog post by a well-meaning young woman racked with doubt about her plans to pursue a graduate degree in Chinese studies; after attending a talk on cultural appropriation, she was unsure that it was morally permissible for a white person to study the field.

This is a skewed and blinkered view. Yes, most cross-fertilization has taken place in a context of unequal power. Historically, interactions between cultures often took the form of wars, colonization, forced or calamity-driven migration and subordination or even enslavement of minority groups. But it is absurd to single out the West as the only culprit. Indeed, there is a paradoxical and perverse Western-centrism in ignoring the history of Middle Eastern and Asian empires or the modern economic and cultural clout of non-Western nations — for instance, the fact that one of the top three entertainment companies in the U.S. market is Japanese-owned Sony.

_{Cathy Young: "To the new culture cops, everything is appropriation", Washington Post, August 21, 2015}

Finally, what is the concept of "Cultural Appropriation" according to common reference works?

cultural appropriation – Cambridge Dictionary noun [ U ] UK ​ /ˌkʌl.tʃər.əl əˌprəʊ.priˈeɪ.ʃən/ /ˌkʌl.tʃɚ.əl əˌproʊ.priˈeɪ.ʃən/ disapproving ​> the act of taking or using things from a culture that is not your own, especially without showing that you understand or respect this culture:

cultural appropriation – Oxford Reference A term used to describe the taking over of creative or artistic forms, themes, or practices by one cultural group from another. It is in general used to describe Western appropriations of non‐Western or non‐white forms, and carries connotations of exploitation and dominance. The concept has come into literary and visual art criticism by analogy with the acquisition of artefacts (the Elgin marbles, Benin bronzes, Lakota war shirts, etc.) by Western museums.

The term emerged during the last twenty years of the 20th cent. as part of the vocabulary of the post‐colonial critique of Western expansionism. One early significant discussion was by Kenneth Coutts‐Smith in ‘Some General Observations on the Concept of Cultural Colonialism’ (1976), where he brings together the Marxist notion of ‘class appropriation’ (the dominant class appropriating and defining ‘high culture’) and what he calls ‘cultural colonialism’, though he himself does not combine the two in the phrase ‘cultural appropriation’. The problem had been identified earlier in the century, though not in these terms, by the New Negro and Harlem Renaissance writers in the USA, who were concerned by the caricature of the African‐American voice and folk traditions in minstrelsy shows and in such popular successes as J. C. Harris's Brer Rabbit stories. On the other hand, Harlem Renaissance writers such as Alain Locke (1886–1954) welcomed the Modernist enthusiasm for African art. In more recent discussion the Modernist engagement with what were seen as primitive art forms (see Primitivism) has been seen as highly problematic. As this suggests, how an artist or writer's use of other cultures should be judged is a matter of interpretation: what one critic might condemn as ‘cultural appropriation’ another would discuss more neutrally as ‘influence’, or even praise as ‘postmodern hybridity’. One of the finest discussions of these issues, although it does not use the term ‘cultural appropriation’, is Michael North's The Dialect of Modernism: Race, Language, and Twentieth‐Century Literature (1994). North is centrally concerned with what has been called ‘voice appropriation’, for example G. Stein's use of an African‐American voice in her short story ‘Melanctha’. ‘Voice appropriation’ has also been debated in terms of gender, as in feminist critiques of Joyce's representation of female conciousness in the Molly Bloom sequence.

Within the field of sociology the most important groundwork has be sought in the works of Pierre Bourdieu:

As the originator of the concept of cultural capital, Bourdieu was notoriously disinclined to elaborate the meaning and significance of con cepts outside of the concrete context offered by empirical research. At the most general level, however, he emphasized that any ‘‘competence’’ becomes a capital insofar as it facilitates appropriation of a society’s ‘‘cultural heritage’’ but is unequally distributed, thereby creating opportunities for ‘‘exclusive advantages.’’ In societies characterized by a highly differentiated social structure and a system of formal education, Bourdieu further asserted, these ‘‘advantages’’ largely stem from the institutionalization of ‘‘criteria of evaluation’’ in schools – that is, standards of assessment – which are favorable to children from a particular class or classes (Bourdieu 1977).
_{Elliot B. Weininger and Annette Lareau: "Cultural Capital", in: George Ritzer (Ed.): "The Blackwell Encyclopedia of Sociology", Blackwell: Malden, Oxford, 2007, p887–888. (Online)}

While the term had been used in academic circles earlier, the concept of cultural appropriation as a target of censure in the public sphere, outside of the obscurity of academia, surfaced in 1992. It wasn't in the US, though, it was in Canada.

The public dispute over whether it was possible to "steal the culture of another" was documented in the Canadian Journal of Law & Jurisprudence the following year, "The Properties of Culture and the Politics of Possessing Identity: Native Claims in the Cultural Appropriation Controversy":

The recent Globe and Mail debate began with an innocuous article calling attention to the Canada Council's (the Council) concern with the issue of cultural appropriation.² The term was defined to mean "the depiction of minorities or cultures other than one's own, either in fiction or non-fiction."³ Following a report from its Advisory Committee for Racial Equality in the Arts, the Council deemed cultural appropriation "a serious issue,"⁴ and acknowledged that "collaboration with minority groups"⁵ was an advisable strategy to avoid perpetuating social stereotypes.

The citation given for the article that sparked the flurry of opinion pieces and letters to the editor was:

• Stephen Godfrey, "Canada Council Asks Whose Voice Is it Anyway?" The Globe and Mail, March 21, 1992 at C-1 and C-15.

The Globe and Mail's archives are available on ProQuest.