Theodore Roosevelt Commemorative Coin Act - Directs the Secretary of the Treasury to mint and issue not more than: (1) 500,000 $1 coins with the image of Theodore Roosevelt as a Rough Rider on one side and an eagle design on the other side; and (2) 500,000 $1 coins with the image of Roosevelt on horseback on one side and a flaming sword of righteousness on the other side. Calls for the coins to be struck at the U.S. Mint at West Point, New York. Authorizes the Secretary to issue such minted coins beginning on January 1, 2006, and to initiate coin sales before such date (2006 will mark the 100th anniversary of Roosevelt receiving the Nobel Peace Prize). Requires surcharges from the sale of the coins minted under this Act to be paid to: (1) the Theodore Roosevelt Association to be used exclusively for educational programs at Sagamore Hill National Historic Site, including for construction and maintenance of a visitor's center and setting up a curatorial chair and purchase fund for the Theodore Roosevelt Collection at Harvard University Library; and (2) the Theodore Roosevelt Medora Foundation to be used exclusively for educational programs at and around Theodore Roosevelt National Park, including construction of the Theodore Roosevelt Badlands Institute in the badlands of North Dakota. Distributes specified surcharge amounts to the Association and Foundation.