Most table service restaurants do not have a dress code whatsoever. The signature restaurants do. And, since you asked, they specifically forbid tank tops.
From the NEW! Disney site:
Men may wear khakis, slacks, jeans or dress shorts and collared shirts. Sport coats are optional.
Women may wear Capri pants, skirts, dresses, jeans or dress shorts.
Not permitted in the dining room are tank tops, swimsuits, swimsuit cover-ups, hats for gentlemen, cut-offs, torn clothing and shirts with offensive language or graphics.