A satellite that could do the job would certainly be extremely useful. However these radars are extremely powerful because they must track object with very low radar cross section (either they are deliberately made that way, or the objects are very small, or both). So these satellites would have really huge photovoltaic arrays or "non-traditional" power sources, and to resolve multiple (dozens, hundreds) of objects at a time, and do scanning, they would also have to have really huge apertures compared to traditional spacecraft.
The reason is not because they are not needed, it is because it would be extremely hard to build, launch, manage, and defend a spacecraft capable of replacing many ground stations.
While the other answer shows Cobra Dane, a US defense radar stationed in Alaska which scans the horizon looking for nuclear missiles and also some satellites, in fact there are necessarily many sites world wide used by the US and certainly many sites used by many other countries.
You can get some idea by going to http://keeptrack.space/ and reviewing the sites. Radar is necessary for many objects, but for some optical tracking is also an important part of the picture.
below: "Aerotel captured this image of three actively maintained geostationary satellites (center) with another satellite nearby (lower left). For this observation, the telescope was staring at one spot, with no tracking movement. Thus, the stationary satellites appear as dots, while the background stars, which are moving at the natural sidereal rate, appear as streaks." From here.