Rebuild Rural America Act of 2021 This bill directs the Department of Agriculture (USDA) to establish the Rural Innovation and Partnership Administration and the Rural Future Partnership Fund to provide five-year renewable rural partnership block grants to certified rural regions to implement locally-developed regional revitalization plans. For purposes of these grants, the following areas may constitute a rural region: a micropolitan statistical area (i.e., at least 10,000 but fewer than 50,000 people); a collection of rural census tracts or counties that fall outside of a micropolitan or metropolitan statistical area (i.e., 50,000 people or more) and that demonstrate evidence of economic, social, and cultural cooperation; or an Indian reservation. To be eligible to receive a grant, a rural region must be certified by its state (or in the case of an Indian reservation, approved by USDA) after having formed a rural partnership council made up of representatives from across different sectors. USDA must provide each rural partnership council with training, education, support, and advice to enhance the technical assistance, research, organizational, and other capacities of the council. The bill also establishes a Rural Future Corps to (1) help rural communities expand critical services such as child care, health, nutrition assistance, education, and job training; and (2) strengthen the capacity of local governments and economic and community development organizations.