Has any country ever annexed territory of another country without physically controlling it?

Well, yes?

Germany perhaps annexed Austria and certainly Czechoslovakia before the troops entered the territory in Nazi times 1938–39.

Germany West also annexed the East without any of its Western military force controlling the territory in 1990. (In case naysayers would like to dispute that terminology: As French Wikipedia confirms…, or Italian Wikipedia suggests.)

The United States annexed Texas in 1845…

Now, arguments will start over the very word "annexation".

This definition is used here:

annexation, a formal act whereby a state proclaims its sovereignty over territory hitherto outside its domain.

Which is the broader and original sense of the word, similar to how French Wikipedia defines:

Annexation is the attachment of one territory to another, usually larger one. This method of acquiring sovereignty differs from colonisation in economic, religious and ideological terms; annexation results in the absolute integration of the annexed territory into the system of the annexer, whether or not this is the result of the will of the annexed populations (plebiscite, self-determination referendum, etc.). In this sense, it is different from a simple occupation.

Which would give plenty opportunity for listing territorial changes, mostly surrounding some wars. Like after World Wars. But when for example Denmark annexed Northern Schleswig, the transfer followed just a legal procedure as was the case when Germany annexed the Saar territory in 1935.

There is a problem with using this word, as some like to interpret into it some kind of (im-)morality or (il-)legality.

Funnily enough, as example over this usually contested word usage for the current events prompting this question: all references on Russian Wikipedia talk about "annexation" ('naturally', as they are all 'Western sourced'?), while the Kremlin —naturally— says 'accession'..

This brings up limits to historical parallelism, as the winners now tend to avoid the word annexation, as it is often meant to imply another definition:

i) Annexation, defined as the forcible incorporation, in whole or part, of an existing state’s territory by another existing state.

— Glen Anderson: "Secession in International Law and Relations: What Are We Talking About?", Loyola of Los Angeles International and Comparative Law Review, Vol 35, No 3, 2013.

That definition might make the so called Texas Annexation not an annexation?

A specialised dictionary even lists:

annexation

The acquisition of title to territory (scil. previously under the sovereignty of another State) by a unilateral act of appropriation by a conqueror State subsequent to subjugation: ‘At no period did conquest alone and ipso facto make the conquering state the sovereign of the conquered territory .... Conquest was only a mode of acquisition if the conqueror, after having firmly established the conquest, and the state of war having come to an end, then formally annexed the territory’: I Oppenheim 699. When, in June 1945, the Allies assumed ‘supreme authority with respect to Germany, including all the powers possessed by the German Government, High Command and any state, municipal, or local government or authority’, they expressly declared that the assumption of these powers ‘does not effect the annexation of Germany’: Whiteman, Digest of International Law (1963), Vol. 1, 325. As it is now accepted that the use of force, except in self-defence, is contrary to international law, so the fruits of an illegal use of force cannot stand in law. So, after the ‘Six Day War’ in June 1967 when Israel invaded the Sinai Peninsula, the West Bank of the Jordan, the Golan Heights, and the unoccupied parts of Jerusalem, the Security Council, in Res. 242 (XXII) of 22 November 1967, called for the ‘withdrawal of Israeli armed forces from territories occupied in the recent conflict’ and emphasized ‘the inadmissibility of the acquisition of territory by war’. Annexation remains important only as a basis of titles to territory acquired when it was permissible. Cf. debellatio. See generally Jennings, The Acquisition of Territory in International Law (1963), Chap. 4.

In British constitutional law and practice, the term ‘annexation’ is employed to connote the incorporation of territory within the dominion of the Crown, or within a particular part thereof, irrespective of its prior status. For a modern example, see the Island of Rockall Act 1982, under which, from 10 February 1972, ‘the Island of Rockall (of which possession was formally taken in the name of Her Majesty on 18th September 1955 in pursuance of a Royal Warrant dated 14th September 1955 addressed to the Captain of Her Majesty’s Ship Vidal) shall be incorporated into that part of the United Kingdom known as Scotland and shall form part of the District of Harris in the County of Inverness, and the law of Scotland shall apply accordingly’.

— John P Grant, J.Craig Barker (eds): "Parry and Grant Encyclopaedic Dictionary of International Law", Oxford University Press, Oxford, New York, 2009, p32.

This definition would make the question as posed self-contradicting, as an annexation would have to always take place after a conquest, and that is 'taking physical control'.

We therefore have to operate with a wider definition of the word 'annexation', or simply state that when applying the stricter definition for it, then the question doesn't make sense.

Just to give a recent one, China claims Arunachal Pradesh as "South Tibet" (Zangnan).

It seems that whenever there's a flare-up in disputes with India, China renames more places in that region (that they don't occupy) to reassert their claims.

Among the 15 places in Arunachal Pradesh that China renamed, eight are residential areas, four mountains, two rivers and a mountain pass, the Global Times report says. China renamed six other places in the same region five years ago. Among China’s names is Zangnan, which means “South of Tibet” in Mandarin.

By the way, if you're more interested in terminology/concepts, one paper that addresses these matters in (a lot) of historical perspective, prefers to speak of "symbolic annexation" in such cases. And of course, China is hardly the first country to do that. The more numerous historical examples are from the "age of discovery". The Treaty of Saragossa, for instance, after virtually dividing the undiscovered (from the POV of the parties) world, stated that any mere discorvery in the forseen division was to be deemed equivalent to possesion... even if discovery was made by the "other side", i.e. if the Spaniards merely discovered an island that was on Portugal's side of the line, it would be as if Portugal took possession of it! Of course, France and England disagreed with this approach, stressing the importance of actual occupation over symbolic annexation, in such claims. One more concrete example (by other countries) was how how the Dutchman Tasman symbolically annexed much of Australia. Of course, the Englishman Cook then had other plans, a century later. Vattel would later theorize that symbolic annexation provides an inchoate title, provided the actual occupation happens in "due and reasonable time". How much [time] that is, remained open to some level of interpretation. (A somewhat interesting case, but much more obscure case of applying this is Bouvet Island, eventually conceded by the British to Norway.)