Of Seneca, Scottish, and English ancestry, he was director of the Rochester Museum of Arts and Sciences from 1924 to 1945, when he developed its holdings and research into numerous disciplines for the Genesee Region.
He was the son of Frederick Ely Parker, who was one-half Seneca, and his wife Geneva Hortenese Griswold, of Scots-English-American descent, who taught school on the reservation.
[1] In 1903 Arthur was adopted into the tribe as an honorary member, when he was given the Seneca name Gawaso Wanneh (meaning "Big Snowsnake").
[2] His grandfather's younger brother (Arthur's grand-uncle), Ely S. Parker, was a Seneca life chief and he had collaborated as a young man with Lewis Henry Morgan on his study of the Iroquois.
He explored his Seneca lineage as a way of connecting himself to a powerful, symbolic past and integrating into twentieth-century American life.
Before going on to college, he spent considerable time at the American Museum of Natural History in New York City, where he was special assistant archaeologist 1901–1902.
However, Parker followed the wishes of his grandfather and attended Dickinson Seminary in Williamsport, Pennsylvania, from 1900 to 1903 to study for the ministry.
During the 1911 New York State Capitol fire, Parker entered the building while it was ablaze and made his way up to the 4th floor in an effort to save priceless historical artifacts.
During the 1930s and the Great Depression, he also directed the WPA-funded Indian Arts Project, which was sponsored by the Franklin D. Roosevelt administration.