GA pilot reported a rapid increase and surging RPMs so they diverted to the nearest suitable airport and landed.

Narrative

Cruise at 8;500 ft. Noticed sudden rapid increase in engine RPM. I reduced the propeller control and found that engine tachometer was hunting from 1700 to 2300 [RPM]. At that point I had an [urgent] situation. Once I knew I had the aircraft stable and I could make to the nearest airport I [requested priority handling]. I was on flight following. I just had flown over ZZZ. At that time flight following said there was no factor with traffic. I did 180 degree turned back toward the runway. I had the runway in sight. Flight following directed me to contact ZZZ Tower. I made two-way communication and [requested priority handling]. They gave me permission to land. I declared that their where three souls on board. They asked if they could be of any assistance; I declined. At that point I had to get rid of some altitude. I circled the airport. The aircraft was flying stable I knew that making it to runway was no problem. I put my gear down reduced the power and didn't touch the propeller control since I had airspeed and altitude. I landed on the numbers. The Tower directed me to the non-movement area.