Looking passed the absolutely insane answer here, no one has even brought up the whole issue of AC vs DC. Batteries are DC, while your fridge that plugs into your wall running on AC. I know they make DC ones, but it isn't like they are interchangeable.
Funny thing, most modern refrigerators use DC motors for their compressors so that they can run at variable speeds, so there's likely an inverter that you could bypass if you know the appropriate voltage. The DC ones for RVs are the same internals, just without the inverter.
Correction: they still use AC motors, but those motors don't use line AC. It goes line AC > rectifier > DC > inverter board > variable frequency AC to run the compressor motor.
Most RV fridges just use DC motors, but there are some that use VFDs and AC motors.
There are DC-AC converters you can use (might be called inverters in English idk), which are pretty interesting circuits. They are used all the time, e.g. to use solar energy
I'm not sure of the max load output on a car battery, but with a 15 amp 1800 watt dc to ac inverter, you probably can run a fridge off one. It probably just won't last all that long.