A320 Captain reports ground conflict in DEN; with fast turboprop; after being cleared into the ramp by Ramp Control.

Narrative

This report concerns a turboprop cutting across the ramp at high speed. We had landed on the east side of the DEN Runway 35R (I think) and after taxiing south on Taxiway L; were turning into the ramp. My First Officer had just communicated with Ramp Tower our position and we were given clearance in. He looked to his right as we made the turn and reported 'clear.' His focus was on the service road and there was no traffic. As I completed the turn westbound onto the ramp; we saw from our right the turboprop cutting across from just inside the entrance and had to slam on the brakes to make sure we did not hit him. I am not sure how close we would have come without braking; but it would have been very close. We contacted ramp and were informed that traffic into the gates are told to give way to aircraft entering the ramp; this plane did not. It scared me how close we came. He was headed to the far east parking edge of the area so there was not much room between his path and the ramp entrance. The ramp has become very congested and there seems to be an increasing number of ops that are not coordinated with Ramp Tower. This really has to be cleaned up before an accident occurs.