21st Century Civilian Conservation Corps Act This bill authorizes the President, in order to relieve widespread unemployment, restore depleted natural resources in the United States, and advance public works programs, to establish a Civilian Conservation Corps to employ unemployed or underemployed U.S. citizens in the construction, maintenance, and carrying on of works of a public nature, such as forestation of U.S. and state lands, prevention of forest fires, floods, and soil erosion, and construction and repair of National Park System paths and trails. The President may extend corps activities to state- and private-owned lands to prevent and control forest fires and floods and attacks of forest tree pests and diseases. The President, based on certain criteria, must give preference to the employment of additional persons in the corps in the following order: (1) unemployed Armed Forces veterans (including Reserve members); (2) unemployed U.S. citizens who have exhausted their unemployment compensation; (3) unemployed U.S. citizens who are eligible for unemployment compensation immediately before employment in the corps, including any additional compensation or extended compensation; and (4) other unemployed or underemployed U.S. citizens. The President is authorized to provide housing and transportation for corps employees. Discrimination is prohibited in the hiring of corps employees.