Rent and Mortgage Cancellation Act of 2021 This bill provides housing assistance during the COVID-19 public health emergency. Specifically, the bill suspends rental and mortgage payments for primary residences through April 1, 2022. The bill also forgives rental and mortgage debt accrued from March 13, 2020, through April 1, 2022. The Department of Housing and Urban Development (HUD) must establish funds to reimburse lessors and lenders for payments suspended or forgiven under the bill. In addition, HUD must establish an Affordable Housing Acquisition Fund to support the acquisition of multifamily housing projects by nonprofit organizations, public housing agencies, cooperative housing associations, community land trusts, and state and local governments. For a five-year period, entities that are approved for such assistance shall be provided the first right of purchase with respect to these projects.