It's not within your rights to knock down a drone, and you wouldn't be able to claim you were defending yourself. Drones have been
shot out of the sky. And then
the guy gets arrested for criminal mischief and wanton endangerment. Not to mention he's likely to have to pay restitution for wrecking the drone
as have others. Discharging a firearm into the air is probably illegal, drone or not. Destroying someone else's property is also illegal. Like it or not,
it is legal for someone to fly a drone over your property in most cases, so you would be liable for destroying someone's drone even if it is hovering over your own backyard. Note that most drones have gopro type cameras which are very wide angle and not that useful for peeping tom stuff unless it was extremely close up; people often cite "privacy" as some sort of catch-all defense for knocking down drones,
but it doesn't work. A photographer with a long zoom lens on the public street can
legally invade your privacy much more effectively.
And lastly, drones are considered aircraft, and it is illegal under federal law to take an aircraft down, period*. I haven't heard of the FAA/NTSB coming after anyone. But if someone got hurt either by whatever weapon or other means one used to kill the drone, or by the drone itself falling from the sky, it wouldn't be that far-fetched.
*
18 USC § 32 says:
And the NTSB has definitively ruled that
drones are aircraft (Administrator v. Pirker).