First of all, there are no descriptive statements of the appearance of Jesus Christ in the Bible that would tell us the length of His hair. Any discussion of the matter has to be based on secondary arguments.
Second, the argument today is often tainted by the assumption of many that the paintings of Christ that came out of the Renaissance of the 1400's and 1500's have some sort of authority. They do not. This Jesus was portrayed with European features and feminine eyes in addition to the long feminine hair. This is the Jesus of their imagination. It is not the Jesus of the Bible.
However, despite a certain level of ignorance, the Bible makes some statements about hair and its length that might be of help to us. I do not include in these statements the directions to the Nazarites (Numbers 6) or the stories of Samson or Absalom. Though these stories and instructions do show us that it was different enough for a man to have long hair that special note was made of the fact. Stories, by nature, do not make a special point of things that are normal, but only of things that are different. Therefore, the instructions for the Nazarites and to Samson to grow their hair long are in scripture because that was not normally done.
One verse of special interest is Leviticus 19:27, which commands the Jews, "Ye shall not round the corners of your heads, neither shalt thou mar the corners of thy beard." This command is given in context of special observances connected with astrology or funerals. However, that does not mean that it had no application for daily living. The Jews believe that this command has to do with the shaving of the temples of the head, a practice once connected with idolatry. This may explain the locks of hair worn by many of the Orthodox Jews today.
However, the verse was probably an injunction against the shaving of the entire head for purposes of idolatry. It is connected with the marring of the corners of the beard. We know the importance of the beards to the Jews because of the shame of those who had half their beards shaved off and the instructions from David that these men tarry in Jericho until their beards grew back (2 Samuel 10:4-5). If their beards were not important, then why not just shave them off entirely and return to Jerusalem? But if they took their beards so seriously, then they probably took the shaving of their heads just as seriously. An exception was made for the Nazarite who ended his vow with the shaving of his head (Numbers 6:18-19).
What does this verse tell us about Jesus? We know that He kept the law. If He was not to shave His head, then He did not do so. But this does not mean He would have long hair in the way seen in modern movies. It only means that it would not shave down to His scalp.
Another passage of importance comes in the New Testament.
1 Corinthians 11:14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
The discussion of this passage is not mainly about the length of hair for men. However, this verse makes a distinction between the length of hair for men and for women. The hair of women is given to them for a covering.
1 Corinthians 11:15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.
This covering is a sign of submission and is seemly on a woman. In fact, short hair that no longer acts as a covering is shameful on a woman.
However, for men to have long hair--hair that provides a covering to the extent that a woman's hair is to be a covering--is a shameful thing. In context, this is something that is certainly not acceptable. It is to wear a sign of submission in a way that destroys the picture of God's line of authority.
Of course, everyone who wants to challenge this wants to know how long is long. The Bible does not give a length in inches. However, there is a principle given. Hair that is a covering is proper for women and improper for men. Hair that is not a covering is proper for men and improper for women. So, the question is, what does it mean for hair to be a covering? It certainly does not mean that the hair is on top of the head. Except for the bald, this is true of both men and women. The Bible clearly teaches in this passage that long hair is a covering and short hair is not.
Though I can see many disagreeing with this, I believe that hair that comes over the ears and begins to lie across the shoulders has become a covering and is therefore long hair. Though this rule is subjective on my part, I have not seen anyone come up with anything better. Clearly, there needs to be a strong distinction. Men should have short hair. Ladies should have long hair. There are varying degrees of short and long. However, there are also lines between the two that should not be crossed. Long hair on a man says to God that this man does not want to fulfill his God-given role as head of the home and leader. He is rebelling against God's order. Short hair on a woman says to God that she does not want to submit to her role as a helper in the home in submission to her husband (or father if she is young). She is rebelling against authority and God's order.
So, how does this help us determine the length of hair for Jesus. Well, for one thing, Jesus was a man's man in His human nature. He was no sissy. Though the Old Testament law kept Him from shaving His hair, the principles given by Paul would keep Him from having womanly long hair as He is often depicted. Since He is the ultimate source of all scripture, it is no argument to say that 1 Corinthians had not yet been written. Also, how could Paul have given the teaching he did on the length of hair if it was known that Jesus had long hair? This simply will not work.
There was no sin in Jesus Christ. Therefore, if we can prove a certain hair length to be God's plan for men, we can prove the length of hair on Jesus Christ. This length, according to scripture, was short but not shaven.