where I live the legal minimum caliber for hunting big game is .243 winchester and I'm 100 percent in favor of such a ruling, that game may be taken humanely. That being said, feral hogs around here are not considered big game in the sporting sense, they're pests and their eradication is encouraged by any means necessary so I dont think there'd be any trouble with using .223 for that if you didn't have something more appropriate at your disposal.
Are you a handloader or are you limited to factory ammo? Factory ammo wise, there are several options available with tough, expanding monometal bullets, such as winchester razorback xt, remington hog hammer, hornady full boar ammunition, and barnes vor-tx ammunition. All of the above should be great for your purposes.
If using these monometal bullets I'd suggest deliberately shooting for the front shoulder. These bullets will have absolutely no problems with insufficient penetration even out of .223, and so you'll want to inflict as much incapacitating trauma as possible and I suspect the conventional wisdom of going for a no-bones double lung shot when using underpowered cartridges will only result in an unnecessarily slow kill in this case because with the .22 centerfires (and even the .24s) you basically have to choose between broad wounding or deep penetration, but it's hard to have both, you've only got so much bullet to work with.
If you roll your own, I would look long and hard at the 75 grain Swift Scirocco II, b.c. over .4 and tough bonded core construction combined with the ability to open up at low impact velocities while hanging together at high ones and a higher s.d. than most .223 caliber hunting bullets.
Good luck and happy hunting.