Answer:
It depends on the fridge. Newer fridges are generally more efficient, so would use less electricity, although size is a definite factor.
There should be sufficient information on the fridge to determine watts, though you may have to calculate. Watts = amps x volts. Volts = 120.
I'd use 120 to avoid underestimating.
In any case, running a fridge only for beer is an avoidable cost unless you make better use of it. Replacing an old fridge and a separate freezer with a newer'' more efficient fridge with useable freezer space probably uses less electricity than 2 older appliances.