Who is the oldest running back in NFL history?

Marcus Allen or Jim Thorpe:

Herschel Walker: Former Football Great Looking to Become Oldest NFL Player Ever
By Ryan Rudnansky (Featured Columnist) on January 25, 2011

At 48 years of age, former football great Herschel Walker has declared that he is thinking about working toward a comeback in the NFL in possibly two years time. Quarterback George Blanda played until he was 48, but he was a kicker the last six years of his career. Players with the greatest longevity in the NFL tend to be quarterbacks and kickers. The oldest running back to ever play in the NFL was Marcus Allen at age 37.

https://americanfootball.fandom.com/wiki/Marcus_Allen

The Pro Football Hall of Fame website lists Jim Thorpe as the oldest running back to play in the history of the NFL at the age of 40. Thorpe played his last down of football for the Chicago Cardinals in 1928.

http://www.bloodyelbow.com/2011/1/26/1957464/herschel-walkers-nfl-comeback-and-the-complicit-media-response
http://www.profootballhof.com/history/stats/40_and_over_club.aspx

I would have to say that at age 48, George Blanda, was the oldest "rostered" running back in NFL history. While he was used as a kicker, he was not always able to actually kick the ball, therefore he had to take his licks as a running back.