C172 pilot reported loss of engine RPM that progressively got worse through the flight and diverted.

Narrative

I picked up the 172 from [the] FBO fresh out of annual for a ferry flight to ZZZ2. My first intended fuel stop was ZZZ3. Climbing out of ZZZ4; leveling at 5;500 ft. to allow the engine to cool before continuing the climb to 11;500 ft. Upon leveling at 5;500 ft. it became clear the engine was under performing. While in level flight the max RPM the engine would produce was 2450 - 2400 RPM. I elected to apply carburetor heat and run a flow check of the aircraft's configuration. I elected to continue the flight as the engine was smooth and no other issues were noted; I decided to begin diverting to ZZZ1 where I'd investigate the low RPM issue as an A&P/IA (Inspection Authority). While determining the proper heading to get to ZZZ1 the RPM began to fall slowly. I ran a checklist and attempted to regain the RPM. The engine RPM then dropped below 2150. I elected to [request priority handling] on frequency and announced my intentions of diverting to ZZZ. The RPM had dropped down to 1100 and would not climb higher no matter the configuration of engine or fuel control. I was set up for a left base for [Runway] XX and announced my intention of landing [Runway] XX as it was the most prominent runway and I already had it in sight. I set up for a left base and after losing most of my altitude in the 12-mile glide to ZZZ I had a shallow left base turn to [Runway] XX. I touched down roughly 500 ft. down the runway; and after slowing the propeller stopped. I rolled to Taxiway XX and began the shutdown checklist and exited the aircraft. No damage to the aircraft or airport property.