Yes. If the petitioner is a U.S. citizen or permanent resident s/he can file a marriage petition on behalf of their same-sex foreign spouse. The eligibility to file a marriage petition for a same-sex foreign spouse and the same-sex foreign spouse’s admissibility as an immigrant will be determined according to the immigration laws applicable to opposite-sex married couples. However, the foreign same-sex spouse of a permanent resident (as opposed to a U.S. citizen) is not considered an immediate relative. As such, the wait time for permanent residence is significantly longer than if the petition is filed by a U.S. citizen.