Is the Cirrus SR22T a turbo-prop? Or does in just have a turbocharger?
It is a turbo charged piston aircraft (much like turbo charged car, the engine is somewhat similar to that found in the older air cooled Porsche 911's (think 930 turbo)). 

Turboprop is generally short for Turbine-Propeller which is a propeller aircraft powered by a turbine engine. 

Turbo charged piston aircraft are piston driven engines with a turbo charger, many often may carry the T or TC designation after the model number. Such as the Piper Saratoga TC or SR22T

In this case we can reference the SR22T's Specs from the website


  Airframe &amp; Powerplant 
  
  Continental TSIO-550-K 315 HP Turbocharged Engine