This is not going to be simple no matter what, but start with the simplest options:
Option 1: 20HP 230V single phase motor. Standard off-the-shelf NEMA single phase motors stop at 10HP 240V then specialty farm duty / grain dryer motors go up to 15-16HP, but as petersonra said, you might find larger if you look around and/or are willing to wait or have a motor shop build one for you. And as he said, expect the FLC to be about 100A, which means your source power transformer feeding the circuit will need to be at least 60kVA, which means in the single phase transformer world, a 75kVA transformer. That's going to be hard to find in a single phase service, a 200A service will typically be fed by a 50kVA transformer, and the next size up for service drops is 400A, which would be a 100kVA transformer. So that's what you would need to have at your single phase service. If you don't, it likely is not going to be allowed by your utility.
Option 2: There are what are called "written pole" motors that run as 3 phase motors, but from a single phase source. It will not really change anything about the FLC issue as far as what is drawn from your source, but it may allow you to start it from a 200A service rather than having to go to a 400A service.
http://www.written-pole.com/singlephase/singlephase.html
Option 3: as mentioned, is to buy a VFD that allows a single phase input at that size, then can run a 3 phase motor. You can still do this with a 200A service. All VFDs are technically capable of doing this, but some can, some cannot because the mfrs did not anticipate this use and did not provide a way to defeat the Phase Loss protection for the input power on 230V drives this large. For this to work, you must at least DOUBLE the size of the VFD compared to the motor, so you would buy at least a 40HP 230V VFD to run a 20HP motor from single phase (because of the higher input current and DC bus ripple from single phase). So problem #2 of this will be that many VFD mfrs do not make a 40HP 230V rated drive, partly because it is so uncommon; generally people using motors that big use 480V.
So option #4: get a 240-480V single phase transformer, about 37.5kVA, and then get a 480V VFD that accepts single phase input (again, be careful) and a 20HP 460V rated motor. You can still do this with a 200A service.
Option #5: get a 3 phase service from the utility.