American Savings Account Act of 2017 This bill amends the Internal Revenue Code to establish a new retirement option for all employees and self-employed individuals to be known as the American Savings Account Fund. This fund operates in a manner similar to the Thrift Savings Fund, which is available to federal employees. The bill establishes an American Savings Account Board of Directors to establish policies for fund investment and management. The board shall select or establish a list of investment funds and options similar to those in the Thrift Savings Fund, among which participants may choose. The board shall establish an American Savings Account Fund Advisory Council to advise the board on matters relating to investment policies. The American Savings Account Fund is tax-exempt and contributions to, or distributions from, it are excludible from gross income.