Uniting Families Act of 2021 This bill establishes a nonimmigrant visa category for the adult alien children of a U.S. citizen who served in the Armed Forces. To obtain a visa, the alien's citizen parent must petition and receive approval from the Department of Homeland Security. The petition shall include (1) DNA evidence establishing the parent-child relationship, (2) a written statement that the parent will provide financial support until the alien receives lawful permanent resident status, and (3) proof of the parent's U.S. citizenship and active duty with the Armed Forces abroad. If the parent is deceased, an adult sibling of the alien may file the petition if the sibling is capable of providing financial support until the alien receives lawful permanent status. Such a petition must include evidence that the petitioner and the alien are siblings, such as birth certificates showing at least one common parent. The period of authorized admission for aliens with the visa is five years, and 5,000 principal aliens may be admitted each fiscal year. Holders of such a visa may adjust to lawful permanent resident status after meeting various requirements, such as being admissible as an immigrant.