Depends on how you define "drone"... there are numerous dedicated supersonic drone targets as well as converted fighters, a few unmanned supersonic X-planes for research, the D-21 and the mother of all UAVs, Buran
If you specify an unmanned (as opposed to optionally manned) supersonic aircraft designed to take off and land under its own power and perform a task that is not research or target representation, it probably is the first, off the top of my head.
Curious to learn how fast it is and what propulsion system it uses!
If so, apparently with the definitive LO nozzle now.