The Catechism of the Catholic Church:

2357
Homosexuality refers to relations between men, or between women, who experience an exclusive or predominant sexual attraction toward persons of the same sex. It has taken a great variety of forms through the centuries and in different cultures. Its psychological genesis remains largely unexplained. Basing itself on Sacred Scripture, which always presents homosexual acts as acts of grave depravity*, Tradition has always declared that 'homosexual acts are intrinsically disordered.**' They are contrary to the natural law. They close the sexual act to the gift of life. They do not proceed from a genuine affective and sexual complementarity. Under no circumstances can they be approved.

2358
The number of men and women who have deep-seated homosexual tendencies is not negligible. This inclination, which is objectively disordered, constitutes for most of them a trial***. They must be accepted with respect, compassion and sensitivity. Every sign of unjust discrimination in their regard should be avoided. These persons are called to fulfil God's will in their lives and if they are Christians to unite to the sacrifice of the Lord's Cross the difficulties they may encounter from their condition.

2359
Homosexual persons are called to chastity. By the virtues of self-mastery that teach them inner freedom, at times by the support of disinterested friendship, by prayer and sacramental grace, they can and should gradually and resolutely approach Christian perfection.

(Emphases not in the original.)

* Cf. Gen 19:1-29; Rom 1:24-27; 1 Cor 6:10; 1 Tim 1:10.
** Congregation for the Doctrine of the Faith, Persona humana, 29 DECEMBER 1975, no 8.
*** This sentence is the translation of the official Latin version published in Briefing, 18 September 1997.