In 1961, he transferred to the University of Tulsa after a 2–7–1 football season, which led to the firing of head coach Bill Meek.
[1] In 1963 after sitting out a year, Rhome starred at Tulsa, passing for 1,909 yards, 10 touchdowns, and suffering 13 interceptions.
[3] Rhome began his professional career in 1965 as the third quarterback behind Don Meredith and Craig Morton; he got a chance to start one game that same year against the Cleveland Browns (17–23 loss).
[5] In 1969, although Rhome was a backup to Bill Nelsen, the information he provided about the Cowboys offense helped the Browns beat them in a 38-14 Conference Championship playoff win.
On August 17, 1971, he was waived after the team decided to keep rookies Dan Pastorini and Lynn Dickey, to back up starter Charley Johnson.
Rhome is also credited with the signing of future hall of fame wide receiver Steve Largent with the Seattle Seahawks.