Graham was drafted in the fourth round, 29th overall, by the Calgary Stampeders in the 2021 CFL Draft and signed with the team on May 18, 2021.[4] He made the team's active roster following training camp and made his professional debut on August 7, 2021, against the Toronto Argonauts.[2] He played in the first seven regular season games in 2021 where he had three special teams tackles.[2] He was transferred to the injured list in week 8 and sat out for the rest of the regular season, but returned to play in the team's West Semi-Final loss to the Saskatchewan Roughriders where he had one special teams tackle.[2][5]
In 2022, Graham again made the team's opening day roster and played predominantly on special teams.[2]