Native American reservations are not states, and - unlike Washington, D.C. - weren’t given any representation by a Constitutional amendment. So Native Americans who belong to a tribe and live on a reservation can’t vote in national elections, can they?
Yes. American Indians and Alaska Natives have the right to vote just as all other U.S. citizens do. They can vote in presidential, congressional, state and local, and tribal elections, if eligible. And, just as the federal government and state and local governments have the sovereign right to establish voter eligibility criteria, so do tribal governments.
Of course Native Americans can vote. See It’s time to recognize the forgotten Americans who helped elect Joe Biden - The Washington Post.
Some Indian Tribes may have varying amounts of sovereignty (Tribal sovereignty in the United States - Wikipedia) and some their own legal systems, and their right to vote was piecemeal until 1924, but they are US citizens and can vote.
The Indian Citizenship Act of 1924, also known as the Snyder Act, (43 Stat. 253, enacted June 2, 1924) was an Act of the United States Congress that granted US citizenship to the indigenous peoples of the United States, called "Indians" in the Act. While the Fourteenth Amendment to the United States Constitution defines as citizens any persons born in the United States and subject to its jurisdiction, the amendment had previously been interpreted by the courts to not apply to Native peoples.