Migrant Accountability Act of 2021 This bill modifies the treatment of unaccompanied alien children, including by transferring functions for the care and custody of such children from the Office of Refugee Settlement within the Department of Health and Human Services (HHS) to the Department of Homeland Security (DHS). Currently, the office provides care for apprehended unaccompanied children, while DHS is typically responsible for detained alien adults. Under this bill, if an immigration officer determines that a qualifying unaccompanied child is inadmissible, the officer may return that child to the child's country of nationality or country of last habitual residence. Currently, only an unaccompanied child who is a national or habitual resident of a country bordering the United States may be returned. The Department of State must negotiate with other countries concerning the repatriation of children. Currently, the State Department is only required to negotiate such agreements with countries bordering the United States. For an unaccompanied child who reaches 18 years of age while in custody, the bill repeals a requirement for DHS to consider the least restrictive setting available for that individual's custody or supervision. Currently, DHS must make such a consideration when such an individual reaches 18 years of age. Before placing an unaccompanied child with a sponsor claiming to be the child's biological relative, DHS must confirm this relationship using DNA technology. A state may refuse placement of an unaccompanied child in the state, including at a federal facility, unless the placement is with a sponsor who is the child's confirmed biological relative.