Roy attended Northeastern University, where he skated with the Northeastern Huskies men's ice hockey team since the 2012–13 season. In his freshman season Roy was honoured when he was named to the 2012–13 Hockey East All-Rookie Team. The following season he was named to the 2013–14 Hockey East Second All-Star Team, and in his junior year he was named to the 2014–15 Hockey East First All-Star Team. He scored a hat trick in his first-ever Beanpot Tournament game as a freshman in 2013. Roy's brother, Derick Roy, also played at Northeastern as a goaltender.[2]
On April 8, 2016, the Anaheim Ducks announced Roy signed his first professional contract on a two-year entry-level contract with the team.[3]
During the 2017–18 season, Roy was recalled from AHL affiliate, the San Diego Gulls, and made his NHL debut with the Ducks against the Vancouver Canucks on November 9, 2017,[4] He scored his first NHL goal against the Boston Bruins on November 15, 2017.[5]
On July 4, 2019, having left the Ducks as a free agent, Roy signed a one-year, two-way contract with the Florida Panthers.[6] Roy began the 2019–20 season assigned to the Panthers AHL affiliate, the Springfield Thunderbirds, registering 14 points through 23 games before he was traded by the Panthers to the Pittsburgh Penguins in exchange for Ryan Haggerty on December 18, 2019.[7] He played out the remainder of his contract to the Penguins in the AHL with the Wilkes-Barre/Scranton Penguins, scoring 10 goals and 21 points in 35 regular season games, before the season was cancelled due to the COVID-19 pandemic.
As a free agent from the Penguins, approaching the delayed 2020–21 season, Roy accepted a professional tryout invitation to attend the Tucson Roadrunners AHL training camp, on January 19, 2021.[8] In the shortened season, Roy led the Roadrunners in scoring with 11 goals and 30 points in 35 regular season games.
On September 17, 2021, having left the Roadrunners as a free agent, Roy continued his career in the AHL in agreeing to a one-year deal with the Laval Rocket, the primary affiliate to the Montreal Canadiens.[9]