2 Cents

Most people say no.

I say yes.

There are two reasons why.

First is his teaching in Matthew chapter 19.

I have heard some New Testament scholars convincingly argue that Jesus' use of porneia in Matt. 19:9 includes homosexuality because it is a catch-all term for any sexual sin.  The best Greek lexicons seem to support this definition.

Since Lev. 18:22 and Lev. 20:13 are OT texts that clearly name it as a sin, homosexuality would be included in Jesus' statement along with such things as adultery, fornication, multiple partners, incest, etc.  A strong example of this argument can be found HERE.

But aside from Jesus' use of the word porneia, we have his statements in verse 4-6:

Have you not read that he who created them from the beginning made them male and female, and said, "Therefore a man shall leave his father and his mother and hod fast to his wife, and the two shall become one flesh"?  So they are no longer two but one flesh.  What therefore God has joined together, let man not separate.

It's very clear that Jesus is teaching on marriage and to him, marriage is between one man and one woman.  So while he does not speak of homosexuality here directly, he does indirectly state that a relationship between two men or two woman does not constitute as marriage.  God is the one who created marriage and he did so when he created the first two human beings - one man and one woman.

However there is a second reason why I believe it is clear that Jesus taught on homosexuality and this one is almost universally overlooked, even among Christians.

The argument is this: If Jesus is God, and everything in the Bible is God's word, then Jesus teaches on homosexuality numerous times throughout the Bible.

First we have to note that Jesus claimed to be God numerous times (John 10:30; John 8:58; John 14:10-11; John 5:18).

Also there is a vast collection of statements outside of the four gospels that ascribe deity to Jesus (Col. 2:9; Phil. 2:6; Gal. 1:1; Rom. 9:5; John 1:1; John 20:28; 1 John 5:20; Heb. 1:3; 2 Peter 1:1, etc). 

So it is very clear the Bible presents Jesus as God.  As Christians we do not worship multiple gods, but one God in three persons - Father, Son, and Holy Spirit - the Trinity.

It is also clear that the Bible presents God as the one who inspired every word of Scripture.  They are the words of God.  (See 2 Tim. 3:16; 2 Peter 1:20-21; 1 Thess. 2:13)

So if all the words in the Bible are God's words, and if Jesus is God, then Jesus did in fact teach on homosexuality in Lev. 18:22, Lev. 20:13, Rom. 1:26-27, 1 Cor. 6:9-11, and 1 Tim. 1:8-11.

So when someone tells me that Jesus did not teach on homosexuality, not only do I see it as an excuse to disregard the rest of the Bible's teaching on the subject, but also a claim that isn't actually true.