Yes, you should be able to run it from and extension cord. Since the refer comes up, that's what I would do until you find the problem with the outlet.
Some suggestions - Check your other AC outlets - see if any others are out. This may give you a clue. Make sure your GFI outlet isn't popped. If the refer is on a slide, look for the point where the AC power cable flexes going to the refrig. Also - reset the breakers by turning them off, then back on even if they don't show popped. Last but not least - those outlets are rather cheap. Sometimes it's the outlets themselves.
Good luck.