I recently installed a small, 1.8 cu. ft. dorm fridge. Tested with a Kill-A-Watt meter running for a few days, the fridge draws about .8 amps. The startup surge is considerably more. Initially, I had it powered with a 600w Samlex pure sine inverter. If I warmed the compressor in the fridge, running it with 120v AC from shore power, the 600w Samlex would run it for the first start. After that, the locked rotor draw would pull the inverter down so it went into protection. I replaced the Samlex 600w with the newer Xantrex 1000w Prowatt pure sine inverter and have had no problems.
Doing the 120v->12v conversion, you will see a draw of 18 amps continuous during the duty cycle. Typical duty cycle in summer temps is about 1/4. If you draw your 90 AH battery down to 45 AH (typical capacity standards), you should be able to run the fridge for about 10-12 hrs. before needing a recharge.