>(Assuming you mean a small drone a citizen could be licensed to operate): Do drones have the ability to stabilize the recoil from a gun powerful enough to kill a pig?
The FAA defines drones as being up to 55lbs, so yes. Most of the off-the-shelf octocopter cinema drones could probably handle an appropriate firearm with some minimal modifications. Now, whether the FAA and ATF will throw a tantrum over a remote control weapons platform like that is a different story...
> whether the FAA and ATF will throw a tantrum over a remote control weapons platform like that
I Am Not A Lawyer, and attempting to build an armed drone without the advice of one one will probably earn you an ATF raid with your dog shot, your spouse sniped, you arrested, your house burned down, a cabinet appointment for the raid leader, and you put on national news with the option for a Netflix documentary 20 years later.
The FAA has a regulation prohibiting the operation of "Dangerous Weapons" attached drones without prior approval [0], so that's your first and biggest hurdle.
A servo-actuated trigger is likely going to get deemed a "machine gun" by the ATF, as it's one firmware tweak (or bug) away from firing more than once per "trigger pull" by the human user. Now if you were to become an NFA firearms manufacturer (Type 07 FFL+Class 2 SOT) you would be manufacturing, demonstrating (remember that FAA approval) and selling hog hunting drones officially.
To reiterate: Do not even think about doing this without actual legal counsel.
The FAA defines drones as being up to 55lbs, so yes. Most of the off-the-shelf octocopter cinema drones could probably handle an appropriate firearm with some minimal modifications. Now, whether the FAA and ATF will throw a tantrum over a remote control weapons platform like that is a different story...