William Arthur Goebel (June 24, 1887 – February 15, 1960) was an American football player.

He played college football at Yale University and was a consensus selection at the guard position on the 1908 College Football All-America Team.

Goebel received his preparatory education at Union High School in Phoenix, Arizona, and in private studies in Cincinnati.

He attended college at Yale University, where he was a member of the football, track and wrestling teams.

As a guard for the Yale Bulldogs football team, he was a consensus first-team selection for the 1908 College Football All-America Team.