For their inaugural season in 1964–65, the team joined the Western Canadian Intercollegiate Athletic Association (WCIAA), alongside its parent institution, Alberta.
They did so in part due to the temporary loss of British Columbia as a league member in order to keep the conference as a viable outfit.
As may be expected for a program who had never before fielded a team, the Dinos got off to a slow start; Calgary went winless in its first three seasons, however, Al Rollins was finally able to lead the club to its first wins in year four.
He promptly led the Dinos to back-to-back Canada West championships, as well as a third trip to the University Cup in 2000, before accepting an assistant coaching position in the NHL.
After the COVID-19 pandemic forced the cancellation of the 2020–21 season, Calgary returned to the top of the conference, winning the league championship in 2023, its first in 27 years.