ARTCC Controller reported C172 was not able to climb to altitude which resulted in controller issuing routing with pilot concurrence to maintain terrain clearance until MVA met.

Narrative

Aircraft X called me off the ground at ZZZ looking for a pop up IFR flight plan out of 056 altitude. Verifying I could communicate with them I asked if they had a flight plan on file; they responded no. I gave them a squawk code and asked if they were qualified and capable of IFR flight. They said yes. I issued a clearance 'leaving 100 cleared to ZZZ1 via direct; climb and maintain 140' for terrain. I asked the pilot for the color of aircraft; souls on board and fuel remaining for the tapes since they didn't file. The aircraft was climbing very slow; and I noticed they were off their course by about 20-30 degrees heading for higher terrain. I asked the pilot to verify they were direct ZZZ1; and they responded with 'we're turning back now; and were unable 140'. I asked if they were able 130 for the MIA (Minimum IFR Altitude) and they responded with no. This should've been communicated with me upon initial clearance; so I could've amended it before they got into the higher terrain. They then tell me they want to change their destination to ZZZ2 while inside a 119 box still climbing out of about 100. I asked if they could maintain their own terrain and obstruction avoidance through 120 and if they were able 120. They said yes to both. I issued a northern heading to the aircraft below terrain to prevent them from entering a 129 box and wanted to get them to lower terrain as soon as possible. Once clear of terrain I gave them a clearance to ZZZ2. Recommendation: No recommendations; this seemed to me like pilot error. I handled it as safely as possible while attending to other traffic conflicts and turbulence reports.