On the Antarctic Peninsula yes, at sites clear of wildlife, and it's one of the better things you can do down there. In South Georgia, no. Camping isn't permitted there at all. The Peninsula restriction to wildlife-free sites came in with the bird flu guidance and that guidance is still evolving, so check the current position for your departure.
This forces a trade worth knowing before you book. If camping is non-negotiable for you, you're effectively choosing between camping and South Georgia. Our guides' verdict is to take South Georgia, on the grounds that camping isn't guaranteed anyway once you factor in the weather, and South Georgia is.
Camping is also snow-dependent, so it works best early in the season and gets harder as sites melt out.
Check this before you commit. It's exactly the sort of restriction that turns into an awkward conversation if it surfaces after you've paid.