Smithsonian American Women's History Museum Act This bill establishes a comprehensive American women's history museum within the Smithsonian Institution in Washington, DC, to provide for: (1) the collection, study, and establishment of programs related to women's contributions that have influenced the direction of the United States; (2) collaboration with other Smithsonian museums and facilities, outside museums, and educational institutions; and (3) the creation of exhibitions and programs that recognize diverse perspectives on women's history and contributions. The bill establishes a council within the Smithsonian Institution to: (1) make recommendations to the Smithsonian's Board of Regents for the construction of the museum; (2) advise and assist the board on the administration and preservation of the museum; (3) recommend annual operating budgets for the museum; and (4) report annually to the board on the acquisition, disposition, and display of objects related to women's art, history, and culture. The council shall have sole authority to: (1) acquire artifacts for the museum's collections, (2) dispose of any part of the collections but only if funds generated are used for additions to the collections, (3) specify criteria for the use of the museum's collections and resources, and (4) preserve and maintain the collections. The museum's director may carry out educational and liaison programs in support of its goals.