The ties on my Atlas code 83 track are styrene, and if those on your turnout are too, it should be easy to repair. I use lacquer thinner as styrene cement, but any liquid styrene cement should work just fine. Use either strip styrene the same size as what's left of the original, or cut a piece out of a sheet of suitable thickness. Trim the broken end square, butt an extension of the proper length to the squared end, and use more of the same material to make a splice plate, then cement it atop both the original and new piece, spanning the joint. Allow 24 hours for the joint to fully harden, then hook up your ground throw as normal. Obviously, you'll need to drill a suitable hole in the new extension, and paint everything to blend in with the original.
Wayne