If marriage was a right, then any two people could simply declare themselves to be married, and that would be it. In fact, a couple who wants to marry first needs to get society's permission, in the form of a marriage license. Then, the couple has to go to someone legally authorized to bind them in matrimony (a clergyman, a justice of the peace, a ship's captain, etc.). Only after that legally authorized person has performed the wedding ceremony is the couple married.
That having been said, any homosexual man can apply for a license to marry a woman, and any lesbian can apply for a license to marry a man. Assuming there are no problems (for example, if nothing shows up in the blood tests), that license will probably be granted. The licensing bureau does not care about the sexual orientation of the applicants. Its only concern is, does the couple meet the qualifications of marriage, that is, is it one man and one woman?