Why is my goldfish swimming in circles?

There may be a water quality issue in your tank. Make sure that you are testing for ammonia, nitrites and nitrates which should be 0, 0, and less than 10 respectively.
If you have readings of ammonia or nitrites, or a high reading of nitrates, you should do an immediate 75% water change. Make sure that the new water you add to the tank is the same temperature as the old water, and be sure to add the correct dosage of water conditioner per the directions on the bottle.

In addition, check the PH of your tank - it should be 7.2 to 7.6 for your goldfish; if it's too low, it could also affect your fish, and the water change should help that as well.