Fraser played as a junior of the British Columbia Hockey League with the Victoria Salsa and the Vernon Vipers, before committed to a collegiate career with the University of Alaska Fairbanks of the Central Collegiate Hockey Association where he scored 114 points in 148 games over his four-year career. Undrafted, Curtis completed his senior year placed second to Kyle Greentree in scoring with 35 points, to leave the Nanooks ranked second in all-time games played. Fraser immediately made his professional debut following college to finish the 2006–07 season in the post-season with the Chicago Wolves of the American Hockey League. Curtis initially signed in the ECHL with the Las Vegas Wranglers for the 2007–08 season and after 4 games with the Wranglers he was signed to a professional try-out contract with AHL affiliate, the San Antonio Rampage on November 15, 2007. Tasked as a grinding role-player in the AHL, Fraser remained with the Rampage for the duration of the campaign, to post 6 points and 85 penalty minutes in 41 games, including a career best two-goal game against the Milwaukee Admirals on January 23, 2008. He was then returned to the Wranglers for the post season and scored 7 goals in 16 games on their run to the Kelly Cup finals. Fraser signed with the Peoria Rivermen for his third professional season in 2008–09. He played in a career high 65 games with the Riverman for 8 points and 90 penalty minutes. In game 4 of the first round playoff series against the Houston Aeros, Curtis had his hand injured by a slapshot from teammate Steve Wagner causing him to miss the Rivermen's last three playoff games and had surgery to insert pins into his broken right hand. Unable to earn a one-way contract with the Rivermen for the 2009–10 season, Fraser was invited to the Wilkes-Barre/Scranton Penguins training camp before suffering a dislocated shoulder in an exhibition game on September 19. He opted to then sign with the Rivermen's ECHL affiliate, the Alaska Aces, which marked a return from his college career days with the UAF. In an injury plagued year Fraser regained some offensive productivity with 13 points in a limited 17 games. On September 20, 2010, Fraser returned to the Aces and was re-signed to a one-year contract. Invited on a try-out to attend the Lake Erie Monsters training camp for the 2010–11 season, Fraser made the Monsters opening season roster and made his AHL return in a 2–1 victory over the Syracuse Crunch on October 9, 2010. On February 17, 2011, he was released from his professional try-out with the Lake Erie Monsters. Prior to the 2011–12 season, on June 28, 2011, Fraser signed a one-year contract with Italian club SG Cortina. The following season, he then joined KHL Medveščak of the Erste Bank Eishockey Liga. During the 2013-14 season Fraser remained in the EBEL, with EC VSV, but announced retirement after the end of the play-offs.
