A member of the Oneida people, he played several sports while attending Carlisle Indian Industrial School and then Haskell Institute.

While attending Haskell, Archiquette captained the football team and was the idol of a young Jim Thorpe, a Native American who went on to be considered one of the greatest athletes of all time.

[6] In his first year with the football team, he appeared at end and was identified by The Inter Ocean as 151 pounds (68 kg), 68.2 inches (5.68 ft), and as being "a harnessmaker by trade.

He was a halfback and received considerable recognition for his ability in slipping away from enemy tacklers by employing a spinning motion that made him almost impossible to hold.

[16]Archiquette was noted in the book Carlisle Vs. Army to be "a fullback who weighed more than two hundred pounds[a] and had astonishing speed for his size.

"[2] The book Carlisle Vs. Army stated that Thorpe, after watching practice: raced back and forth over the empty field, zigging here, zagging there, trying to emulate his idol.

Thorpe nodded his head excitedly, so Archiquette led him to the harness shop and sewed some leather scraps together.

He stuffed the makeshift ball with rags and handed it over to a grinning Thorpe, who couldn't take his eyes off his new prize.

[19] He was known for his "strong arm and keen accuracy"; in one game against the Kansas YMCA, he was reported to have made two shots from underneath the opposing basket across the entire court.

"[19] In one game during the 1900–01 season, Archiquette performed what biographer Rob Raines called the first known instance of a player using the zone defense.

[22][23] He returned for the 1903 season, with the Lawrence Daily World reporting that he had "played with the Indians for so long that they can hardly get together in a game without him.

[35] After leaving Haskell in 1905, he joined Green's Nebraska Indians, an all-star barnstorming baseball team, where he played for several years.

[36] He briefly was a coach for the Haskell basketball team, implementing some of the zone defense techniques he pioneered.

[19] After two years as a clerk at Carlisle, Archiquette was transferred in 1906 to the Osage Indian Agency and settled in Pawhuska, Oklahoma.