I have found entirely the opposite; it's very strongly correlated with spelling ability - or so it seems from my necessarily few observations, of course. I know some excellent mathematicians who write very stilted prose, and a few make more grammatical errors than I'd have expected, but they can all at least spell well.

I know many very intelligent good spellers, and several very intelligent mediocre spellers, and one or two very intelligent apparently incorrigibly atrocious spellers. I don't know any moderate-intelligence good spellers, a few moderate-intelligence atrocious spellers, and quite a few quite a few moderate-intelligence mediocre spellers. I don't know very many dumb people socially, and mostly don't know how good their spelling is as they don't write much. People I met on the Internet don't really count, as I filter too much on spelling ability to begin with.

I have the opposite impression, but now that I have that correlation it's hard to make further unbiased observations.