No, Jesus did not become divine when he received the Holy Spirit. Jesus was born divine; he did not become divine. In fact, at his conception he was divine. We do not know exactly how it works, but the Scriptures clearly tell us that the Word which is God (second person of the Trinity) became man. In Christian theology, we call this the hypostatic union. It is the teaching that in the single person of Christ are two distinct natures: God and man.  This is how Jesus was conceived.  He did not become divine later.

“In the beginning was the Word, and the Word was with God, and the Word was God… 14 And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten from the Father, full of grace and truth,” (John 1:1,14).

These two verses clearly tell us that the “word was God” and that “the Word became flesh and dwelt among us”. Therefore it would be erroneous to say that there was a change in the nature of Jesus in which his humanity became divinity. Furthermore, it would be erroneous to say that when he received the Holy Spirit that he became godlike at that time.

Jesus did not become more divine after receiving the Holy Spirit

Jesus was not partly divine and then became more divine when he received the Holy Spirit. He received the Holy Spirit in the same way we do because Jesus, like us, is human (Colossians 2:9; 1 Timothy 2:5). Since he was under the law (Galatians 4:4), he was subject to the requirements that the law advocated which included worshiping God. In other words, he had humbled himself and cooperated with the limitations of being a man.  In Philippians 2:5-8, it says the following…

“Have this attitude in yourselves which was also in Christ Jesus, 6 who, although He existed in the form of God, did not regard equality with God a thing to be grasped, 7 but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men. 8 Being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross,” (Phil. 2:5:8).

In this section of Scripture, we see that Jesus emptied himself and humbled himself to the point of death. This set of scriptures is often the focal point of many discussions because it mentions the position that Christ assumed in the incarnation. Now, we don’t know fully what it meant for the word to become flesh, but we can see that it involved a kind of emptying. It did not lessen the divinity of Christ. But, we would say that Christ cooperated with the limitations of being a man.

So, Jesus was born divine. He was and still is both man and God. He has two distinct natures: divine and human. He did not increase in his quality of divinity when he received the Holy Spirit nor did he reduce his divinity when he became man.