I run my workshop off a generator so the plasma will be maxing the generator out on full power, I can't run a compressor at the same time.You must have a power supply to run the plasma cutter so why not just run a normal compressor from that?
If you want an accurate number then you need to find out:
Working pressure of the fridge compressor,
Water capacity of the gas tank
Consumption and operating pressure of the plasma cutter.
The gas tank capacity will be stamped into it somewhere, the other info should be in the manual for the plasma but you might have to find a service manual or something for the fridge.