Pilot reported a sudden drop in engine RPM; popping noises; and significant vibration while in cruise flight. The pilot diverted to the nearest airport for a safe landing.

Narrative

I was undertaking a solo cross country flight from ZZZ1 to ZZZ2 in order to continue to build hours in preparation for gaining my Commercial Pilots License.The aircraft preflight all appeared normal. The engine had 6 quarts of oil and the fuel was topped off to full at ZZZ1. During the preflight engine run-up checks the magneto checks were all well within tolerances and there was no unusual engine vibration or roughness observed.Prior to departure from ZZZ1 I picked up VFR flight following from ZZZ Approach. The take-off was uneventful and upon reaching a cruise altitude of 4500 ft. MSL I reduced power and leaned the mixture out to Rich of Peak. Approximately 40 minutes into the flight I was instructed to remain east of the freeway for reported skydiving activity over Lake A by ZZZ Approach; which I complied with. When I was approximately 4 NM east of ZZZ the engine RPMs dropped suddenly to about 2000 RPMs. Some popping noises were heard coming from the engine and I felt significant engine vibration. I [requested priority handling] with ZZZ Approach and told them I was experiencing engine problems and needed to land. I looked for my best landing spot. I Squawked XXXX and ran through my initial flows for power loss in flight. Applied carb heat; checked the fuel position; enriched the mixture full; cycled the throttle and checked the magnetos and primer. I looked over at my emergency checklist to my side and double checked I hadn't missed anything. I decided ZZZ airport was the safest option so proceeded direct to the airport and was switched over to the Unicom frequency for the private airport. I contacted Unicom and told them I was in a left downwind for the north runway and needed to land. They advised me it was a dirt strip; which I was aware of. I proceeded to keep the engine power at idle and make a short approach to ensure I made the runway in the event of complete engine failure. As I assessed I still had some potential engine power available if I really needed it; I elected to keep the engine running as I had no indications of fire. Upon landing I was able to turn around and taxi a short distance before shutting the engine down to prevent possible further damage.After landing the airport manager informed ZZZ Approach I was safely on the ground. I followed up with my own call to ZZZ Approach shortly afterwards to confirm they required no further information from me.Post flight inspection of the engine by a qualified A&P at the airport revealed a bent push rod for the #1 cylinder.