Civilian Climate Corps Act of 2021 This bill requires the Departments of the Interior and Agriculture, in coordination with other relevant federal agencies, to enter into an interagency agreement establishing a Civilian Climate Corps, to be operated in accordance with the National and Community Service Act of 1990 and the Domestic Volunteer Service Act of 1973. A project carried out by the corps must (1) prioritize efforts to assist disproportionately impacted communities, or be carried out in partnership with a qualified youth service or conservation corps; (2) be coordinated with tribal and Native American communities to protect natural cultural resources; and (3) accomplish one or more of particular objectives such as conserving, monitoring, and restoring public land and water to help mitigate and adapt to climate change.