He was originally signed as an undrafted free agent by the Dallas Cowboys in 1995, following a career at University of New Haven where he won the 1993 Harlon Hill Trophy.
He attended Spring Valley High School before playing college football at University of New Haven.
He gained 389 yards his senior season of high school as a fullback, and was recruited to New Haven as a linebacker.
[1] He convinced the team to put him at tailback, and made an immediate impact when started, setting the all-time school record for single-game rushing yards, with 262 in a 30–31 loss vs.
Graham earned an increased role in his sophomore year, and broke the single-season New Haven record for rushing yards.
His coach, Mark Whipple, commented, "We want to put the football in Roger's hands 20 times a game.
"[8] Graham would become the school's all-time leading rusher in his fifth sophomore appearance, following a 192-yard game against Central Connecticut.
[9] He helped the school achieve its sixth consecutive 1992 win following a performance that included 236 yards rushing, and three touchdowns, against American International.
[10] He was named Division II honor role after carrying 17 times for 140 yards with two touchdowns, helping New Haven win its ninth game of the year.
[11] He would finish the season with 1,717 rushing yards, helping New Haven make the playoffs and break the record previously set by him in the last year by 775.
In his junior season, Graham would rack up over 1,600 yards, being rated one of the county's top running backs.
[14] On ceremonies held on December 10, 1993, Graham was awarded the Harlon Hill Trophy, given to the best player in Division II, after beating out finalists Tyrone Rush and Jamie Pass.
[16] Following his award-winning junior season, Connecticut governor Lowell Weicker declared February 2, 1994, "Roger Graham Day".
[20] By October 27, Graham trailed only Walter Payton, one of his favorite players, as all-time Division II scorer.
[24] Graham did not have an injury until his final college game, but "the timing couldn't have been worse", as it affected his combine statistics and made his draft projection go from round 3 to undrafted.