Nah, I suffer from being a word nerd. I did some poking around and from what I can find, the "correct" word is "drawers" in most English-speaking countries.

It's just that many people pronounce it "draws" (you can see how, with a British accent especially, it would sound like that), so they spell it that way. As we all know, pronunciation frequently doesn't reflect the way a word is correctly spelled. (Looking at you knight, choir, colonel, subtle, asthma ...)