Civilian Climate Corps for Jobs and Justice Act This bill establishes a Civilian Climate Corps Program and generally revises benefits provided to national service program participants. The bill establishes a Civilian Climate Corps to operate (1) a national climate service program; and (2) a national climate service grant program to help communities respond to climate change and transition to a clean economy, including through reducing carbon emissions. The bill also provides for allowances for participants in certain national service programs, including the Volunteers in Service to America (VISTA) program and the National Civilian Community Corps. The bill expands the exclusion from gross income, for income tax purposes, to exclude amounts received as educational awards or benefits and income attributable to discharges of student loan debt under the National and Community Service Act of 1990.