This answer is based on the doctrine of original sin as held by at least Lutheranism. Related question: Are we born sinners?
There are, in fact, two important questions here. One explicit, one implicit.
The explicit question
Does God create some people heterosexual and others homosexual?
As other answerers have meritoriously pointed out, the Bible depicts homosexual acts as an abomination.
Romans 1:26-27 (ESV)
For this reason God gave them up to dishonorable passions. For their women exchanged natural relations for those that are contrary to nature; and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error.
1 Corinthians 6:9 (ESV)
Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality,
Leviticus 18:22 (ESV)
You shall not lie with a male as with a woman; it is an abomination.
Remember what God said when he looked at the creation, after creating man:
Genesis 1:31 (ESV)
And God saw everything that he had made, and behold, it was very good. And there was evening and there was morning, the sixth day.
No, I don't believe God created anyone homosexual, triggered to do what he sees as an abomination. But do read on...
The implicit question
Are some people born heterosexual and others homosexual?
How God created us and how we were born are two entirely separate matters. God created us perfect, but in the Fall of Man, Adam and Eve chose sin and the entire humankind after that is born with original sin.
Psalm 51:5 (ESV)
Behold, I was brought forth in iniquity,
and in sin did my mother conceive me.
We are born sinners, even though God did not create us such.
I don't know how this actually works. It might be that all of us are born perverted in some way: one prone to murder, one to lie, one to steal, one to be proud, one to have extramarital sex, one to have homosexual sex. Being born in such a way wouldn't make the action right, though more understandable.
Praise the Lord for carrying the burden of our sins, for we are indeed full of sin!
God did not create any of us sinners, yet we all are.
Some of us might be born homosexual. The Bible doesn't clearly state either way, and we're still waiting for conclusive scientific research.