Yes.

Just as with heterosexual couples, your same sex spouse may apply for and obtain U.S. Citizenship three (3) years AFTER having obtained lawful permanent residence (LPR) status, as long as your spouse has no criminal convictions which would bar him/her from US Citizenship, has committed no actions which would act as a bar to US Citizenship (such as a prior false claim of US Citizenship or voting in a state or federal election prior to obtaining US Citizenship).

The application is filed on a form N-400, and must be accompanied by a copy (front and back) of your spouse’s “green card”. All of the questions must be answered extremely carefully and accurately. Any false answer or incomplete answer may result in denial of the application for citizenship.

If US Citizenship is based upon marriage to a USC (US citizen), and at the time of the application and approval remains married to that person, your permanent resident spouse can obtain US Citizenship in THREE YEARS.

For all other lawful permanent residents the N-400 Application for US Citizenship may not be commenced before the person has FIVE(5) years of lawful permanent residence.

After the WINDSOR decision which struck down the federal law that prohibited federal benefits to same sex marriage members, made by the US Supreme Court on June 26, 2013, on equal protection grounds via the14th and 5th to the U.S. Constitution, same sex couples enjoy the same federal benefits and protections under US law as do heterosexual couples.