No.

While some tribal enrollment documents or IDs may be used to prove U.S. citizenship in certain scenarios, they typically are not enough to prove citizenship alone.
Native Americans born within the United States, including on sovereign tribal lands, are U.S. citizens. But tribal membership itself does not equate to U.S. citizenship: For example, a person born in Mexico could be a member of a tribe in Arizona but would not be a U.S. citizen without going through the naturalization process.
Each tribal nation establishes its own enrollment requirements. Federal agencies, such as the Department of Homeland Security or Citizenship and Immigration Services, determine which tribal documents can be used to verify U.S. citizenship.
The Arizona Center for Investigative Reporting partners with Gigafact to produce fact briefs, or quick-response fact checks, about trending claims relating to Arizona.