Military Citizenship Act of 2003 - Amends the Immigration and Nationality Act respecting naturalization through service in the armed forces to: (1) reduce the required service from three years to two years; and (2) prohibit the imposition of a naturalization fee.Provides for overseas naturalization proceedings for members of the armed forces.Directs the Secretary of Defense to prescribe a policy that facilitates the finalization of naturalization proceedings for members of the armed forces, including priorities for emergency leave and air transportation.