Could be a bad GFI.

Try the unit on another non GFI plug.
Usually it is not recommended to use a GFI with a fridge.
Compressors can create electrical noise which can trip a GFI.

If it is a true current leakage to ground the most likely culprit is the compressor.
Check it with a meter.
Use a high meter scale when checking the windings to ground.
Other likely possibilities would be the condenser or evaporator fans.
These could be checked by unplugging them to see it it still trips the GFI.

Here is a good link with how to check things.
Refrigerator Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com