The answer to the question is yes and no. In order to more properly address this question, we have to learn a little biblical theology and a little logic. First of all, Jesus has two natures: divine and human. This is called the hypostatic union.
Second, as a man Jesus was made under the law (Galatians 4:4) and was made for a while little lower than the angels (Hebrews 2:9). As someone who is under the law and who is a good Jew as Jesus was, it would be necessary for Jesus to obey the law and worship God (in this case, the Father – see John 17:5).
Third, we have to be careful with the word "God." We don't want to commit the logical fallacy of equivocation where the meaning of a word changes as we are using it. Let me clarify.
Please read the next two sentences carefully and notice who the word “God” is used for in each.
- The Trinity is the teaching that the one God of all existence, consists of three divine persons: The Father, the Son, and the Holy Spirit.
- The Father is God, the Son is God, and the Holy Spirit is God.
In sentence number one, the word “God” is a quantitative, dealing with how many gods there are. In sentence two, the word "God" is qualitative, dealing with nature; that is, the nature of divinity.
So when someone asks if Jesus has a God, there is a huge risk here of the fallacy of equivocation or confusing the quantitative sense with the qualitative sense. This is why it is important to understand biblical theology, so that a proper answer can be given. Here it is:
Yes, Jesus, who is the second person of the Trinity and divine by nature, worshiped God the Father as a good Jew who was under the law (Galatians 4:4). Remember, Jesus had humbled himself and emptied himself in the incarnation and was cooperating with the limitations of being a man while acting under Jewish law (Philippians 2:5-8). Also, Jesus is still a man (1 Tim. 2:5; Col. 2:9) and will be a man forever (1 Cor. 15:28; Heb. 6:20; 7:25). Therefore, it can be said that Jesus, the man, had someone he would call his God, and his was a reference to the Father. Since he will always be a man (as well as divine), he will always have someone he will call his God -- but this is in reference to God the Father. That does not mean that Jesus does not share the same divine nature as God the Father, since the Bible says that Jesus is also God made man (John 1:1,14; Col. 2:9; Heb. 1:8).