This question is sharper than a previous one, to which it is linked by an answer, considered as incorrect by @uhoh. The formulation "Has there been used to discover?" is more challenging than a "can it be used for detection?". The latter can be answered by a few engineering facts on capability, with caveats added for feasibility (to water down enthusiastic misinterpretations). The former requires in priniciple an exhaustive survey of the discoveries so far. Here is the full database, in case you are brave enough to take up the challenge.
A sharp question is not necessarily better. In my opinion the base question is "CAN RADAR be a better technique for searching for all NEOs, especially the hard-to-detect ones, yet potentially hazardous for humanity?".
This in turn calls for several interrogations: (a) Why do we need a better early-warning system?; (b) How have discoveries been performed so far and what are the short-comings?; and (c) Which new technologies could be in our road-map (RADAR among them)?
Answering these questions satisfactorily are far beyond my capability (and may need a full book). But here are some indicative clues that I have found:
-WHY DO WE NEED AN EARLY WARNING SYSTEM?
It suffices to link these two facts:(a) the 2013 impact; and (b) the goal set by the US congress in the 2018 bill, Section 321.
In Section 321, the set goal is to detect and catalog 90% of NEOs of size >140 meters, ONLY by the Year 2033. To put this into perspective, the Chelyabinsk meteor has an estimated diameter of ~20 m, a “too small” size to be contemplated for this goal. And yet, a 500Kg fragment of its meteorites has been found(!). Would it not be important to be able to detect the meteor, even a couple hours before impact?
-HOW DISCOVERIES HAVE BEEN PERFORMED SO FAR?
Mostly passively, ground-based detections, in the visibility and infrared spectra. “Passive” means that the illuminator is not under our control (but “free”. Here, the Sun or the object’s radiation itself, if it does radiate strongly enough). The process involves taking “pictures” of a small portion of the sky at different times. Something that is “near-earth” must move in the captured pictures if the timing is set adequately. Basically it is a movement-detection, passive process.
The main drawback of this process is that the favorable geometry puts the Earth between the illuminator and the target. Chelyabinsk is an example of an unfavorable geometry.
-WHY NOT “ACTIVELY” OR SPACE-BASED?
“Active” means that we control the illuminator (time, direction, intensity, modulation), but the downside is that it is not free. You can play with this tool to have a first idea of the RADAR limitations.
“Space-based” means that we put the detector in-orbit, possibly around the Sun.
Note that the US Congress Bill of 2018 mentions space-based technologies, BUT NOT RADARS (sorry to fans of Arecibo and like).
- MY ANSWER TO “HAS THERE BEEN AN INSTANCE OF ASTEROID DISCOVERY BY RADAR”?
Discovery of objects on known trajectories (such as moons of known asteroids, of multi-body asteroids), YES.
Discovery of an object with unkown trajectory, very likely NO (see above discussions). For NEOs, it is possible to scan the database of discovered objects and have an definitive answer. The OP should know the existence of this database (otherwise the question is open-ended).