Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
No, homosexual relationship is totally prohibited in Islam.
Islam considers homosexuality as a sexual deviation leading to a perverted act which goes against the natural order Allah intended for mankind. It is a corruption of the man�s sexuality and a crime against the opposite sex. Therefore, the Islamic shariah strictly prohibits the practice of this perverted act. This is mentioned in many places in the holy Qur�an.
The story of the people of the prophet Lut who were addicted to this practice, is the best example.
Allah Ta'ala says,
Prophet Lut (�Alayhis-sal�m) said to his people: �Verily, you do sodomy with men, and rob the wayfarer! And practice all wickedness in your meetings,� (Al-Ankabut, 29:29).
And he said to them: �Of all the creatures of the world, will you approach males, and leave those whom All�h has created for you to be your wives? Nay, you are a trespassing people!� (Al-Shu�ara�, 26:165-166)
But their answer to Prophet Lut (�Alayhis-salam) was: �Bring us the Wrath of Allah if you are telling us the Truth.� (Al-Ankabut, 29:29). And so Allah gave them the punishment they deserved: �And We rained on them a rain of torment. And how evil was the rain of those who had been warned.� (Al-Shu�ara�, 26:173).
Sayyiduna Abdullah bin Abbas and Sayyiduna Abu Hurairah (RA) report from Rasulullah [Sallallahu-Alayhi-Wasallam]:
"Accursed is he who commits the act of the nation of Loot (Alayhimus-Salaam)." - Mishkaat p.313.
For more information please view this article by Mufti Zubir Bayat: http://www.direct.za.org/articles/Social/homosex/homosex.html