In the latter part of his career, he was signed as an injury replacement or to provide competition during training camps for a number of teams.

Graham played college football at Virginia Tech and was named to the first-team All-Big East Conference in all four seasons.

[9] On October 30, Graham was invited back for a tryout after kicker Rian Lindell missed two field goals in a 24–20 loss to the Miami Dolphins.

[14] The following week, in a game against the Green Bay Packers and after being on the team for only two days, Graham missed a 24-yard field goal inches to the right with 13 seconds remaining that would have tied the score.

With the Bengals in 2003, Graham played in all 16 games and set a franchise record by making 88% (22-of-25) of his field goals.

[17] In 2004, Graham narrowly missed matching his previous season's accuracy mark, finishing the year 27-of-31 (87.1%) on field goals.

This included a game against the Baltimore Ravens where he set a franchise record by kicking 7 field goals (the second highest total in NFL history).

In the Wild Card playoffs on January 9, 2010, Graham missed two field goals in the Bengals' 24–14 loss to the New York Jets, including a 28-yard attempt that would have cut the score to 24–17 late in the fourth quarter.

After the game, Marvin Lewis commented on Graham's missed field goals stating "It is a shame, and it killed us.

[20] On October 16, 2010, the New York Giants signed Graham due to an injury to kicker Lawrence Tynes.

In his first game, in Week 10 against the Pittsburgh Steelers, Graham was 2-for-2 on field goals but missed one of four extra point attempts on the night.

[24] On August 23, 2011, the Dallas Cowboys signed Graham due to a hip injury to David Buehler, but did not make the roster after being passed on the depth chart by rookie Dan Bailey.

[31] On April 15, 2013, the Cleveland Browns signed Graham to replace Phil Dawson who left as a free agent.

[32] On August 31, he was surprisingly released, even after making all of his pre-season attempts, leaving the Browns with no kicker on the roster days before the season began.

[33] On September 9, 2013, the Pittsburgh Steelers signed Graham due to a hamstring injury to Shaun Suisham.

Hartley had been cut from the Saints after he had struggled in the 2012 and 2013 seasons and the final straw came when he missed two close range field goals in a game against the St. Louis Rams.

On January 4, 2014, Graham went 4-for-4 including a 32-yard game winner as time expired to propel the Saints past the Philadelphia Eagles in the wild-card round of the 2014 playoffs.

[36] However, the following week during the divisional round game he missed two field goals versus the Seattle Seahawks.

[37] On his first miss, from 45 yards, holder (and backup quarterback) Luke McCown had the laces facing the wrong way.

[40] A few days later on September 2, it was announced that the Saints had waived quarterback Ryan Griffin to make room for the re-signing of Graham to their 53-man roster.

[45] On November 26, 2015, Graham signed with the Atlanta Falcons as a replacement kicker, after Matt Bryant injured his leg.

[48] On February 6, 2017, Graham announced his retirement from the NFL at the age of 39 to pursue jobs as a special teams coach.