McGraw played collegiately as a walk-on under head coach Bill Snyder at Kansas State University from 1997-2001. He was a non-scholarship redshirt his freshman year of 1997. McGraw became a starter in 2000 after getting action as a back-up in 1999. In 2000 as a junior, he was a Big 12 Honorable Mention by the AP and coaches. He led the Wildcats to a Cotton Bowl victory over the Tennessee Volunteers. 2001 would be McGraw's final season, a season that Wildcats struggled to a 6-5 record, after a loss to the Syracuse Orangemen in the 2001 Insight.com Bowl.
On March 29, 2007, McGraw signed a two-year contract with the Kansas City Chiefs. On September 13, 2009, McGraw scored his first touchdown after blocking a punt against the Baltimore Ravens. McGraw also had an interception when the ball was tipped in the air and he caught in the endzone for a touchback. This would also lead to a 39-yard Hail Mary touchdown from Tyler Palko to Dexter McCluster.