I've got to head to work so I have to keep this short...
4 amp/hr is not a particularly effecient model of refrigerator.
Jason nailed it...watts is watts.
Somewhere on the unit (and usually in the manual) there *has* to be the load rating for the applicance; in other words, how much power it draws while running. This is manadated in regulations so it has to be there somewhere (and must be on a plate/sticker on the unit).
Find out what it draws when it's running on AC power; multilply amps times volatge and you have watts. Takes those watts and divide by 12 (close enough) and you know what the load in amps is on the DC side.
Then...depending on where you live you can guess as to how long the refrigerator will run each day (based on air temp, how often you open and close the thing, insulation around it, etc). If you decide that's 50% of the time (12 hours per day) and you're pulling 4 amps when it's running then you need 48 amps from your batteries to support the refrigerator each day. To do that you should have a 137 amp-hour battery; probably a group 31 deep cycle would get the job done in a pinch.
Obviously if the unit only runs 30% of the time (about 7 hours) you'd only need 28 amp hours and that only needs an 80 amp-hour battery (about a group 27).
Most high efficiency units now use the Danfoss compressors; the smaller refers typically the model 35 (there are others on the market now). They'll pull as little as 2.5 to 3 amps on the DC side. They're used in the Norcold DE series which has no propane system. They also don't require the unit to be level; usually only within 35 degrees or so (it's only the absorption model refers that have to be level, or nearly so). They aren't inexpensive but neither are the high efficiency home units based on the same compressors.