Military Personnel Citizenship Processing Act - Amends the Homeland Security Act of 2002 to establish an Office of the FBI Liaison in the Department of Homeland Security (DHS) which shall monitor and assist with Federal Bureau of Investigation (FBI) functions related to expeditiously processing naturalization applications filed by or on behalf of: (1) members and former members of the Armed Forces; (2) current spouses of active Armed Forces members and surviving spouses and children of U.S. citizens who died while on active duty; or (3) deceased individuals eligible for posthumous citizenship.

Authorizes appropriations.

Amends the the Immigration and Nationality Act to require that United States Citizenship and Immigration Services (USCIS), within six months of receipt of a naturalization application filed by a member of the Armed Forces, or the spouse, surviving spouse, or child of such member: (1) process and adjudicate the application, including background checks; or (2) provide the applicant with an explanation for the inability to meet such deadline and an estimate of the adjudication date.

Requires that: (1) the Director of USCIS report annually to the appropriate congressional subcommittees identifying all such naturalization applications that have not been processed and adjudicated within one year because of background check delays; and (2) the Comptroller General report to Congress regarding the average length of time taken by USCIS to process and adjudicate naturalization applications filed by members of the Armed Forces, deceased members of the Armed Forces, and their spouses and children.

Repeals the provisions of this Act five years after the date of enactment of this Act.