Apple Cider Vinegar can clean a shower head by soaking the shower head in Apple Cider Vinegar overnight.
But what works best for cleaning shower heads of calcium and other hard water deposits is just plain ole white distilled vinegar.
I remove my shower head from my shower every 6 months and then fill a bowl with some white distilled vinegar and then soak the shower head overnight in the white distilled vinegar and by morning the hard water deposits and calcium come off and out of the shower head easily.
So if you want to use Apple Cider Vinegar to clean your shower head you can but using plain white distilled vinegar is the best for cleaning shower heads.