You probably have a modified sign wave inverter, and need a pure sign wave inverter to run the high torque refrigerator motor.
The pure sign wave inverters are a bit more expensive, and probably a 600+ watt rated one would be needed to run a 1C for a couple of seconds.
That means #2 wire with a 100 amp fuse. At least 4 batteries to supply the power, so the voltage does not dip below 11.5 volts on compressor start up.
I have 4 each golf cart batteries with a total capacity of 440 amp hours at 12 volts. This holds about 2,500 usable watts before depleting the battery below 50% capacity. You don't want to go below 50% very often, or the battery will not last very long.
You also need a way to recharge the battery from time to time. Solar is the way to go.
Fred.