Congressional Commission on Civic Service Act - Establishes the Congressional Commission on Civic Service to make recommendations to Congress for: (1) improving the ability of individuals to serve others; (2) training leaders in public service organizations to better utilize individuals committed to national service and volunteerism as they manage human and fiscal resources; (3) identifying solutions to the barriers that make it difficult for some individuals to volunteer or perform national service; and (4) building on the foundation of current service and volunteer opportunities. Specifies topics to be addressed by the Commission, including deterrents to service, a mandatory service requirement, and the need for a public service academy.