Is the concept of theurgy used in bible or any Christian scripture?

Is the concept of theurgy used in bible or any Christian scripture?

The art or technique of compelling or persuading a god or beneficent or supernatural power to do or refrain from doing something - Theurgy

The concept in itself seems to be dealt with in the Sacred Scriptures, but not rather explicitly, but rather implicitly, since it constitutes an abomination in eyes of the Ancient Israelites and Christians.

For example, the wearing of amulets in not seen in a favourable light when taken into a relationship to Pagan gods.

But firstly, let us see what is theurgy in truth?

As regarding the Merriam-Webster definition used in the question; it is a modern condensed definition which they claim was first used in 1569! However its' origins came from the 4th century. It is by far an inaccurate definition of what theurgy truly is!

Here follows a more complete understanding of the term in a religious context.

Theurgy (θεουργία, literally “divine work”) is best understood as a collaborative effort between human beings and the gods. The word was first used by the Chaldean Oracles in the second century CE and became fully elaborated in the ritual philosophy of the Neoplatonist Iamblichus (died c. 325 CE). Unlike the earlier system of Plotinus, which stressed the importance of contemplation (θεωρία) to attain mystical union (ἕνωσις) with the One, theurgic Neoplatonism also emphasizes ritual. Various ritual techniques serve to purify the vessel (ὑποδοχή) of the theurgist and enable his or her ascent (ἀναγωγή) to the divine source. Theurgic rituals utilize various divine sumbola (σύμβολα: symbols, tokens, passwords) and sunthemata (συνθήματα: tokens, signs, passwords, signatures), which consist of natural materials (stones, plants, incense, etc.), divine names, numerical constructs, and other ritual structures. A gradual process of ritual purification and ascent brings about the realization of the divinity within the individual (what Iamblichus calls “the One of the soul”). One way this can be understood is a shift in an individual’s perspective from the mortal to the divine. Therefore, the supposed body-soul “dualism” of Plato’s Phaedo and Phaedrus can be reconciled with the overall monistic system of the Timaeus (and of Neoplatonism in general). Matter is “connatural” (συμφυής) with Soul, Soul with Intellect, and Intellect with the One. Theurgic ritual is the complementary moment of reversion (ἐπιστροφή) to the demiurgic procession (πρόοδος), understood to be a continuous cyclical movement. By coming to understand the hidden structures of the universe, the theurgist participates (μετέχει) in its ongoing creation.

With this definition in mind, the following biblical references may be helpful:

• And say, Thus says the Lord God: Woe to the women who sew magic bands upon all wrists, and make veils for the heads of persons of every stature, in the hunt for souls! Will you hunt down souls belonging to my people and keep your own souls alive? - Ezekiel 13:18
• Therefore thus says the Lord God: “Behold, I am against your magic bands with which you hunt the souls like birds, and I will tear them from your arms, and I will let the souls whom you hunt go free, the souls like birds.” - Ezekiel 13:20
• In that day the Lord will take away the finery of the anklets, the headbands, and the crescents; the pendants, the bracelets, and the scarves; the headdresses, the armlets, the sashes, the perfume boxes, and the amulets. - Isaiah 3:18-20
• Moreover, Josiah put away the mediums and the necromancers and the household gods and the idols and all the abominations that were seen in the land of Judah and in Jerusalem, that he might establish the words of the law that were written in the book that Hilkiah the priest found in the house of the Lord. - 2 Kings 23:24
• Moreover, you took your sons and daughters whom you had borne to Me and sacrificed them to idols to be devoured. Were your harlotries so small a matter? You slaughtered My children and offered them up to idols by causing them to pass through the fire - Ezekiel 16:20-21
• But there was a man named Simon, who had previously practiced magic in the city and amazed the people of Samaria, saying that he himself was somebody great. They all paid attention to him, from the least to the greatest, saying, “This man is the power of God that is called Great.” And they paid attention to him because for a long time he had amazed them with his magic. But when they believed Philip as he preached good news about the kingdom of God and the name of Jesus Christ, they were baptized, both men and women. Even Simon himself believed, and after being baptized he continued with Philip. And seeing signs and great miracles performed, he was amazed. - Acts 8:9-13

Addendum:

The art or technique of compelling or persuading is the Wikipedia’s definition that I believe the OP is after, and that's the definition that I am using for this answer. "Crying out" is not compelling. "Art or technique" really implies magic/ritual, which "crying out" is definitely not.

the art or technique of compelling or persuading a god or beneficent or supernatural power to do or refrain from doing something

Would this count? Abraham here is trying to persuade God to avert His wrath from Sodom, convincing God to agree to more and more merciful terms:

Here, God decides to end Hezekiah's life, but Hezekiah pleads with God to consider his loyalty, and so God rolls back His decision:

And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed. [Genesis 32:28 KJV]

I would suggest that prayer is a means of 'persuading' God. And this is one example.