God's displeasure with acting out on homosexuality is depicted as early in the Old Testament as:
Genesis Chapter 19, The story of the destruction of Sodom and Gomorrah. Two angels in disguise visit the city of Sodom and are offered hospitality and shelter by Lot. During the night, the men of Sodom demand that Lot hand over his guests for homosexual intercourse. Lot refuses, and the angels blind the men of Sodom. Lot and his household escape, and the town is destroyed by fire.

    Leviticus 18:22 ("You shall not lie with a male as with a woman: such a thing is an abomination.")

    Leviticus 20:13 ("If a man lies with a male as with a woman, they have committed an abomination; the two of them shall be put to death; their bloodguilt is upon them.)

    Romans 1:26-27 ("For this reason God gave them up to dishonorable passions. Their women exchanged natural relations for unnatural, 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 their own persons the due penalty for their error".)

    1 Corinthians 6:9-10 ("Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither the immoral, nor idolaters, nor adulterers, nor sexual perverts, nor thieves, nor the greedy, nor drunkards, nor revilers, nor robbers will inherit the kingdom of God".)

    1 Timothy 1:8-10 ("Now we know that the law is good, if any one uses it lawfully, understanding this, that the law is not laid down for the just but for the lawless and disobedient, for the ungodly and sinners, for the unholy and profane, for murderers of fathers and murderers of mothers, for manslayers, immoral persons, sodomites, kidnappers, liars, perjurers, and whatever else is contrary to sound doctrine".)

    Jude 7 ("Just as Sodom and Gomorrah and the surrounding cities, which likewise acted immorally and indulged in unnatural lust, serve as an example by undergoing a punishment of eternal fire".)

(From the Catechism of the Catholic Church)

Catholic Tradition (2357)
    Homosexuality refers to relations between men or between women who experience sexual attraction to others of the same sex. Although homosexuality has taken many forms, its psychological source remains largely unexplained. Catholic Tradition (based on biblical texts) has always taught that "homosexual acts are intrinsically disordered" (Congregation for Doctrine of Faith). They are against the natural law, are closed to the gift of life, and do not proceed from a genuine sexual complementarity. Under no circumstances can they be approved.

Called to Chastity (2358-2359)
    The number of persons with homosexual tendencies is not negligible. They did not choose their condition and they must be accepted with respect. All unjust discrimination must be avoided. They are called to do God's will and to unite their sacrifices to the Lord's sacrifice on the cross.
    Homosexual persons are called to chastity and to a self-mastery to gain inner freedom. If supported by disinterested friendship, prayer, and the sacraments they can approach Christian perfection.

See Also: from Catholic Answers
Why Jesus Doesn’t Need to Speak About Homosexuality
Does the Catholic Church Condemn Homosexuals?
What the Early Church Believed: Homosexuality