State Admission Day Recognition Act of 2010 - Requires the Architect of the Capitol (AOC) to honor a state's anniversary of admission to the Union by flying its flag over the Capitol each year on that anniversary.
Requires the AOC to fly the first such flag on the first December 7 which occurs after the enactment of this Act, in honor of Delaware's anniversary, the first state admitted to the Union.
Authorizes the House Committee on House Administration and the Senate Committee on Rules and Administration to promulgate jointly such regulations as may be appropriate to carry out this Act, including regulations permitting the AOC to honor the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, Guam, the U.S. Virgin Islands, and the Northern Mariana Islands by flying the flag of each such jurisdiction over the Capitol each year on an appropriate date for that jurisdiction.