I suppose you could, but the design would have to be changed to account for the different conditions on the Moon.
And it wouldn't be the most practical solution to the power problem.
You're talking about an environment where there's no atmosphere to refract or reflect sunlight, with no hydrological cycle to produce clouds that could block out sunlight, and that's tidally locked to the Earth, meaning its days and nights are two weeks long.
It would be more efficient, all things considered, to simply locate your planned colony near the lunar terminator and build solar panels along the terminator which are able to periodically adjust their orientation so they're always facing the Sun.
That would give you a power source which didn't require you to constantly supply your own fuel, didn't come with the additional risks of using nuclear material or require nearly as much hazardous maintenance and upkeep, didn't require any specialized hazardous waste disposal facilities or procedures, and which could continue supplying you with partial power if one or more panels go down, whereas if you have to scram your reactor, you're left with nothing but whatever battery power you have in reserve until you're able to repair the reactor and bring it back online.
So yeah, you could build a nuclear reactor on the Moon, but there are other, more efficient solutions for energy production that don't require you to ask the question "I wonder what would happen if tons and tons of rocket fuel carrying several hundred pounds of uranium fuel rods exploded over a major population center," so why would you?