12 gauge would be fairly strong medicine, but it has to be close in. If the drone is a stabilized gun platform with the ability to aim decently well (<4 MoA @ 100 yards) that's not going to be a winning battle.
Taking the discussion back to reality, almost all uses of drones at the moment are via suicide ("wire guided COTS missiles", you might call them), or just plain old recon. There are probably still plenty of grenades dropped from hover as well.
For those uses, there's a fairly decent approach ["missile"] or hover ["bomber"] stage that is probably plenty vulnerable to autonomous PDS via 12 guage medicine.
Tracking / detection could even be passive, partly acoustic, partly EO/IR, with only a small fire control radar if you really want it.
