21st Century Civilian Conservation Corps Act This bill authorizes the President, until the end of FY2022, to establish and operate a Civilian Conservation Corps to employ unemployed or underemployed U.S. citizens in the construction, maintenance, and carrying on of public works, 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. If there are insufficient funds to employ all U.S. citizens in the corps, the President must give preference in the hiring process to (1) unemployed veterans, (2) workers who have exhausted their unemployment compensation, and (3) other unemployed workers eligible for unemployment compensation. The President may provide housing and transportation services for corps employees. The bill prohibits discrimination in the employment of corps employees, but individuals convicted of a crime may not be employed in the corps.