I think a dab of vinegar would do just as well as the orange peel, although you might end up smelling of fish & chips. More seriously though, the whole antioxidant scam is just that a scam. We need free radicals and oxidizing agents in our system’s they are the first line of defense against pathogens. If you try to mop them all up with antioxidants, then you could make yourself more prone to diseases (skin or otherwise).
That said, there are billions of natural biochemical reactions taking place in our bodies every day that produce oxidants, you’d have to be popping pills all day long to mop them up.
Moreover, those pills would have to be 100% effective to eradicate enough oxidants to have any effect. Acne is a disease, it’s not caused by bad diet, unclean skin or anything else you can treat with herbal infusions or slices of cucumber. Generic pimples are a different matter (it’s like confusing the common cold with influenza).
More on the ebeauty site here