He began his studies at Stanford in civil engineering but soon quit to rethink his major. When he returned to Stanford it was as a liberal arts major with an emphasis on philosophy. He graduated in 1927. He later attended the University of California for his Ph.D., granted in 1938. His specialization was culture change and applied anthropology.
As a student, Barnett did field work among the American Indians of Oregon, Washington, and northwestern California, particularly the Yurok, Hupa, Yakima, and several small groups of the Oregon coast. Some research concerned diverse ethnological matters but focused primarily on the Indian Shaker religion and the potlatch. The latter was the subject of his doctoral dissertation.
From 1947 to 1948, Barnett conducted field research on the indigenous people of Palau.
Barnett continued to study American Indians in California and the Pacific Northwest and displaced communities in the Pacific. He served as a visiting lecturer for the American Anthropological Association from 1960 until 1961. He spoke at college campuses that did not have anthropology departments, trying to spread his knowledge of anthropology. Barnett became an emeritus professor at the University of Oregon in 1971 and officially retired in 1974. After his retirement Barnett worked on writings and publications up until the time of his death May 9, 1985.
During World War II he stopped teaching to participate in the Far Eastern Language and Area Training Program of the University of California at Berkeley. Here he trained volunteer service men to be effectively gain information from native informants to help the war effort. In 1944 he began working with the Ethnogeographic Board to provide scientific information about human and natural resources of world areas. He later began working with the War Document Survey in the Pacific to give advice about documents that the U.S. government was acquiring from other governments during the war.