Turco hasn't played since finishing last season with the Chicago Blackhawks. He must pass through waivers and if he does, he won't be eligible for the playoffs since he signed after the trade deadline.
The 36-year-old, who was most recently playing for EC Red Bull Salzburg of the Austrian hockey league, agreed to a one-year contract worth $900,000.
The veteran goaltender has played in 538 regular season games with the Dallas Stars and Blackhawks. He was 273-165-43 with a .910 save percentage, 2.35 goals-against average and 41 shutouts.
Meanwhile, Rask is expected to be unavailable until the post-season after he sustained the injury during Saturday afternoon's game against the New York Islanders.
The 24-year-old had registered a .929 save percentage and 2.05 goals-against average in 23 games this season.