I’ll take shot at even; still, has the War of the Machines started yet?
I’m going to hazard that airborne drones are strictly air-to-ground and that the Ghost X-9 is still a few years off.
But here’s a video of presumably public footage aired in 2009 of an autonomous ground vehicle identifying, tracking and destroying another (obviously also autonomous, or at least radio-controlled) tank.
It also depends on your definition of “drone”. Many people (including myself) found out about automated AA cannons after this unfortunate event, so it’s plausible that automated AA has destroyed automated aircraft in digital anger before.
That would require two nations advanced enough to have drones engaged in a battle of air superiority. Thankfully, there is no such conflict. It’s really only a matter of time, though, before air superiority drones are used for patrolling borders and takes a shot at a reconnassance drone or something. You’ll probably see it happen in Iran, Israel, or Southeast Asia in the near future. Of course, nowadays Eastern Europe is shaping up the same way.
Drone is now the general media’s term for unmanned aircraft of certain types. In (English speaking) militaries, ‘drones’ are unmanned target a/c. A/c like eg. Predator/Reaper/Global Hawk are not called drones by their users but rather Unmanned Aerial Vehicles or Systems. OTOH just in literal English, a guided missile is also an unmanned a/c, especially if it uses the air for lift and control (ie not a strictly ballistic missile). So if we’re making up definitions, like the general media has with the word ‘drone’, we might call SAM’s or AAM’s ‘drones’ too, in which case such missiles definitely have shot down other unmanned a/c, often using guidance systems not under direct human control (‘fire and forget’ like infrared or active radar guidance)
But in the sense you surely mean for ‘drone’, an unmanned reusable combat a/c which itself launches expendable weapons, none AFAIK has yet launched such a weapon against another similar umanned a/c in combat. However at least at one time the USAF planned to add the capability to Reaper UAV’s to launch Stinger (normally a man portable SAM, but also used as an air-air missile by helicopters). It might have, or might still, test this capability which would surely be against a(n actual) drone, an unmanned target a/c.
But in general there seems a consensus that air to air combat is too complicated a task for either autonomous or remotely piloted (modern combat UAV’s are some combination of those two things, depending on the task or stage of flight) unmanned a/c for now. The US (N or AF I don’t recall) actually did test BQM-34 drones (still common jet target drone) in air combat v manned a/c way back in the 1970’s. The drone has always had the inherent advantage of being able to maneuver without consideration of g-load a human pilot can withstand. But other than that the remote pilot did not have the situational awareness to deal with a manned opponent, and even with the vast increase in computing power since, no unmanned vehicle could yet handle the task autonomously either.
Drone v drone combat (using the colloquial definition of drone as Corry El suggests) need not be for air superiority–I would think of it more as an interdiction mission. I can imagine insurgents packing some kind of armament on a six-rotor drone and trying to take damage a Predator. Maybe not today, but soon.