C182 pilot reported entering a runway without an ATC clearance. The pilot quickly exited the runway; but the aircraft on final approach had to perform a go-around.

Narrative

Ground directed me to Cross RWY XXR from the Run Up area at Taxiway '1' and hold short at RNY XXL for takeoff clearance. I crossed RWY XXR and crossed the hold line for RNY XXL and momentarily entered RNY XXL. I immediately realized my mistake and made an abrupt and quick 180 degree turn back across the hold line for RNY XXL. As I made my 180 degree turn back to the hold line; I could see an aircraft on a short 1/2 mile final. I was back across the hold line prior to that aircraft crossing the runway threshold; but was later told by Ground that the landing aircraft had to go around due to my runway incursion. That day was the end of a very long flying day and weekend for me flying multiple missions each day and did not have a restful sleep the night before. I'm sure fatigue was a factor as was my single pilot status for that last ferry flight to home base. At the time of the incident; ZZZ was experiencing a very heavy workload with multiple planes waiting for departure at the ends of both runways as well as some intersections. As I was in line at the hold line of the Non-Movement Area; I requested an intersection takeoff from Taxiway '2'; right in front of hold line (There was already one aircraft holding there). That request was denied; and I was told to proceed to the end of RWY XXR.If I had been granted the intersection takeoff at XXR; or more importantly; if I had paid proper attention to the Hold Line; no incursion would have happened. I think in my mind at the moment; I may have been thinking of line up and wait; but as I entered the runway it immediately occurred to me that it was a Hold Short directive and I took Immediate action to correct my error. Brain Fart; Fatigue; no second pilot to double check me; a bit of pressure to help with the heavy workload and probably a bit of impatience were all contributing factors that day.