The fact that you probably have a 20 Amp circuit is a good thing.
If the plug you are describing
Looks like this , it is a 120 VAC 20 Amp plug. They make it like that so you do not plug a 20Amp appliance into a 15 Amp outlet. If you look at the 20 Amp receptical, you will notice that you can plug a 'normal' 15 Amp plug into it as well as a 20 Amp (with the single sideways plug) plug. The circuit is sufficient to power either 20 Amp or 15 Amp appliances.
Electricians will quite often run 20 Amp circuits with 15 Amp recepticals on it so they can put more recepticals on each circuit.
If the breaker for the circuit you want to use is a 20 Amp breaker and the wire is 12 gauge (It has to be 12 gauge or thicker for a 20 Amp breaker or it is not per NEC code), then all you need to do is swap out the receptical.
See here for wire gauges vs breaker sizes.. There is absolutly no problem plugging a 20 Amp appliance into a 20 Amp circuit.
The bad thing here would be to put a 20 Amp receptical in a 15 Amp circuit. A 15 Amp circuit would most likely only have 14 gauge wire. If you try to pass too much current through a smaller wire, then the wire could heat up, melt the insulation, and catch fire. Make absolutly certain you are on a 20 Amp circuit before installing a 20 Amp receptical.
Do make sure that you do not have lots of other appliances pluged into every receptical on the circuit. The NEC makes assumptions that the residential customer will not have something plugged into every receptical on the circuit. A circuit with eight lamps plugged into it will not trip the breaker. If you put three space heaters and a fridge on the same circuit, then it will start tripping the breaker. This is not really dangerous as the circuit breaker is still protecting the wire, just an annoyance. If you find you are tripping the circuit then just un-load it some.
All that being said, this is a $8.00 job if you are on a 20 Amp circuit and feel comfortable swapping out the receptical yourself. The little instruction book that comes with the receptical will show you how to hook it up. Also, consider buying one of those outlet testers with the three lights on it to confirm the polatity and grounding is correct (and check all your other recepticals in the house too).
As earlier posters mentioned, confirm on the back of the UPS that it is indeed 120 VAC.