They can if they were born a US citizen ("native born"), are at least 35 years old and have lived in the US for 14 years. Specifically, while Native American reservations are considered sovereign soil for many purposes of US Law, for determination of US citizenship, they are no different than any US state territory.
The requirements for Native Americans to be President are no different than any other US citizen.
Charles Curtis (January 25, 1860 - February 8, 1936) the 31st Vice President of the United States (1929-1933) was a Kaw Nation Native American Indian. On his mother's side, Curtis was a descendant of the chiefs White Plume of the Kaw and Pawhuska of the Osage. From his mother, Curtis first learned French and Kansa. As a boy lived with his mother and her family on the Kaw reservation. In 1902 when the Kaw tribe was disbanded by the federal government, as enrolled tribal members, Curtis (and his three children) received about 1,625 acres (6.6 km²) of Kaw land in Oklahoma. Before he was Vice President, he was a United States Senator from Kansas from 1907 to 1913 and then 1915 to 1929.
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Yes, I hope an American Indian can become president one day, which would bring this nation full circle. Susan
become slaves
Jim Thorpe (link below) was probably the first American Indian to play pro football. He played professionally with the Pine Village Pros in Indiana in 1913 and later went on to become the first president of the NFL, where he also played for the Oorang Indians (an all-American Indian team) in Ohio.
Oklahoma Territory
It was an India Indian, not an American Indian.
American Association of Physicians of Indian Origin was created in 1984.