Man, absolutely you can hunt deer and stuff with it! Many people out there I find are too uptight about what type of caliber to use on hunts as if every game animal requires its own special caliber. Though I understand their point of view, I don't agree with it completely.

It's all about ethics, problem is most people think their interpretation of what is ethical is the one and only right way to do it.

If a caliber can effectively kill the game animal IMO it's ethical. For example, I wouldn't think it's ethical to use a .22 on a big game animal like a moose or bear or something as you're more likely to cause non-lethal wounds. Some folks say they've hunted deer with a .22 but in order to do that effectively you'd probably need to be quite close and get a head shot - I wouldn't use a .22 on a deer.

The 7.62x39 for the SKS though is a big enough projectile to hunt deer with IMO. It's larger than a 5.56 and is kind of like the 308.

One thing to note though is the effective accuracy of an SKS and that round isn't going to be good at longer ranges. I've never used my SKS to hunt as I opt for my more accurate guns to do that with but if I were and that was the only thing I had, I wouldn't take a shot past 100m with my iron sights (maybe 200m with good optics).

All in all, yeah you can totally use it for hunting as long as you're shooting at a comfortable range you've practiced accurately up to and target animal is of the appropriate size (deer is a yes in that case).

Hope that helps :)