We do! Many satellites, including the Voyager missions, use something called an RTG to power their electronics. They essentially just sap heat from a decaying chunk of plutonium, though, which isn’t quite a nuclear reactor. Those are really heavy and we don’t have an excellent way of turning electricity into thrust right now (ion thrusters run fine on solar energy, for the most part), so there’s not an incentive to get a large reactor into orbit.
There’s also some concern about launching large amounts of radioactive materials from Earth into space, since a malfunction could mean scattering that stuff over a very large area if the rocket breaks up in the atmosphere.
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