... It used to be a 480 volt 3 phase compressor that they changed out to a 240 volt single phase motor.
Bingo, we have a winner!
3HP 230V single phase motor is 17A in the NEC chart, so you would use a breaker of around 40A (250% of the motor FLC from the NEC chart). A 20A 2 pole breaker was probably OK when it was a 480V 3 phase motor, but it is way too small now.
You need to check your conductor sizes too. If they still have 12ga wire, that's possibly a no-go as well. 17A x 1.25 = 21.25A, it might need #10 conductors if there is no motor OL relay or the motor is not internally protected, you might even need #8 if the only thing on that circuit is the 40A breaker.
Side issue: Torque is torque, 3 phase or single phase. HP = Tq x RPM / 5250, it doesn't matter if the HP is derived from 1 phase or 3 phase. So if the old 460V 3 phase motor was also 3HP, the torque from the single phase 240V motor would be the same (assuming also that the RPMs are the same).