I have just placed a fridge on my patio. My problem is the GFI trips. I believe it is when the compressor kicks on. I have one GFI with a reset. I think it is at the beginning of the run. The only thing I have tried is resetting the GFI.

It is working as it should. You have a voltage leak in the refrigerator. I could tell you to replace with a regular outlet but that doesn't fix the issue.

Basically, A GFCI device works by sensing an imbalance of current.

More than likely what is happening is that the "Inrush current" of the motor or compressor starting causes the GFCI to trip.

Slight possibility that the GFCI device is to sensitive but I really doubt that.

Can you run a temporary cord to the refrigerator from a non GFCI receptacle and see if the tripping goes away?

Also, if the GFCI circuit is only 15 amps, The breaker itself may be the problem. Moving to a 20 amp circuit may be your only solution. To move the entire circuit to 20 amp would require new conductors (12 AWG) or install a separate circuit for just the outdoor receptacle. You would still need to run 12 AWG and get a 20 amp breaker, but the cost would be contained because of the reduced distance.