The 32-year-old defenseman has signed a one-year, two-way deal that pays $800,000 in the NHL and $350,000 in the AHL with the Wranglers.
Tinordi was drafted by the Canadiens in 2010, he has played for several teams, including the Blackhawks, Bruins, Coyotes, Penguins, Predators, and Rangers, splitting time between the NHL and AHL.
Tinordi brought physicality, ranking second in hits on the team. While he could make the Flames' roster if they opt for seven defensemen, he'll likely end up in the AHL.