Graziani was a seventh round pick of the Atlanta Falcons in the 1997 NFL Draft. He played for the Falcons for three seasons. During his NFL career, he threw for 999 yards, two touchdowns with eight interceptions. He also had 16 carries for 51 yards. Also, during his one-year tenure with the Cleveland Browns, he played for the Barcelona Dragons, of NFL Europe, in 2000.
Graziani signed with the Los Angeles Avengers prior to the 2001 season. He completed 23 out of 37 passes that season for 262 yards, seven touchdowns and one interception. He became the starter in 2002 as he completed 282 out of 467 passes for 3,568 yards, 67 touchdowns, and 1 interception. In 2003, he completed 304 of 495 passes for 4,290 yards, 96 touchdowns, and 15 interceptions. In 2004, he had his finest season as he completed 333 of 510 passes for 4,265 yards, 99 touchdowns, and five interceptions.
Prior to the 2005 season, Graziani signed with the Philadelphia Soul and became the highest-paid player in the league. He completed 328 out of 555 passes that year for 4,272 yards, 90 touchdowns, and 15 interceptions as Philadelphia had a disappointing 6-10 season. In an injury-riddled 2006, he completed 232 of 389 passes for 2,981 yards, 41 touchdowns, and 11 interceptions, but Philadelphia went 9-7 and made the playoffs for the first time ever. Through Week 4 of the 2007 Arena Football League season, Graziani had completed 75 of 116 passes for 1,041 yards, 24 touchdowns, and only three interceptions. At the time, the Soul were undefeated at 5-0. In Graziani's third start against the Colorado Crush he threw for eight touchdowns topping out over 300 yards and only one interception. He suffered a shoulder injury in week 6, and was unable to play for the next five games. He came back in week 12 against the New Orleans VooDoo and went 7-of-15 for 81 yards and four touchdowns. The Soul won the game 78-34.
During Week 1 of the 2008 season Graziani set the Soul franchise single game record for most touchdown passes in a game (nine). In Week 3, he suffered a sprained ankle. He was scheduled to return Week 7 against the San Jose SaberCats, but before the game it was decided he wouldn't play. He returned Week 8 against the Columbus Destroyers, but left the game with an injury. He briefly returned against the Dallas Desperados, but left the game with a concussion. He did not play in the AFL after that.