Call the manufacturer of the compressor, and see if they offer a single phase motor that can swap directly in.
The other option is a 'variable frequency drive', but converting single to three phase you need to oversize the VFD by 100%. (ex 1hp single phase motor would require a 2hp VFD)
ABB ACH550 UH 04A6 2 AC HVAC Drive 4 6 Amp 3 Phase 0 500Hz | eBay
Also, you will be limited to 208v motor, so if you have a 480v 3phase motor you are out of luck.