Promoting National Service and Reducing Unemployment Act This bill provides FY2020 supplemental appropriations to the Corporation for National and Community Service (CNCS) for Operating Expenses, Salaries and Expenses, and the Office of Inspector General. The CNCS must use the funds in a manner that (1) increases to 500,000 the number of national service positions approved under the AmeriCorps program, and (2) gives preference to programs that propose to use full-time national service positions.