Cats like to eat grass/plants every once in a while. I know mine is a royal PITA--he's not allowed outside, but he always seems to get his way. The little bastard always seems to outsmart people. Until I found out that if I rip some grass out of the yard and bring it in to him, he'll stop trying to get out the door, either mostly or completely... but that's only a temporary solution. As soon as the grass is gone, or if he *really* wants out (ie. a nice day), he's back in action. The other downside is that, as much as he likes it, it often makes him throw up. Maybe you could use this method to attempt to keep the cat away from your peppers? To be honest though, I wouldn't trust a cat near any plants; it's just too risky. If you can put the plants in a location the cat is unlikely to try to reach (ie. too difficult to get to or away from the cat's points of interest), that might work.
If your cat likes grass, there's so-called "cat grass" (oats) meant for cats (it's supposed to be good for them). I wouldn't grow it where the cat's able to reach though; you'll have a huge mess before the grass is even able to reach one inch tall. But obviously, this is out of the question for now, because it takes about a week to reach a decent height.