Yep you can my mother is a boss of the American Red Cross In my city.....in fact I went to give blood today but my iron was too low and didn't pass, they're rarely ask questions unless they are fresh cuts but if not not necessarily. I just simply reply I have/had a problem and am now working on it can't speak for the whole foundation of the A.R.C. Across the states but assuming from where I stand it won't be a big deal