Marriage does not guarantee that a person can become a citizen, but it is mentioned as a special case here: http://www.uscis.gov/naturalization
“Spouses of U.S. Citizens
Generally, certain lawful permanent residents married to a U.S. citizen may file for naturalization after residing continuously in the United States for three years if immediately preceding the filing of the application:
*
the applicant has been married to and living in a valid marital union with the same U.S. citizen spouse for all three years;
o
the U.S. spouse has been a citizen for all three years and meets all physical presence and residence requirements; and
o
the applicant meets all other naturalization requirements.
Because of the infernal DOMA law, the USCIS might not recognize a gay union, but given that you would have to be married for at least 3 years prior to applying, there is a fair chance the law will be overturned by then. Obama wants it struck down.