Fortifying America's Intellectual Property Rights (FAIR) Act - Amends the Trade Act of 1974 to establish in the Office of the United States Trade Representative the position of Assistant United States Trade Representative for Intellectual Property Rights, with primary responsibility for: (1) intellectual property matters relating to trade agreements and the negotiation and enforcement of intellectual property provisions of any such agreement to which the United States is a party; (2) identification and investigation of foreign countries that deny adequate protection of intellectual property rights or that deny fair market access to U.S. persons that rely upon intellectual property protections; and (3) monitoring the extent to which U.S. trading partners protect and enforce intellectual property rights of U.S. persons.