Probably not, but it depends on how big your head is. I'm 6'1" and take a 7 5/8 hat, but it isn't really related to your height. I knew a guy who was about the same height as me who could never find a hat that fit his head.
Hats are a lot like shoes, even if you know your size, it can vary from one manufacturer to another. Go into the store and try them on.
Here's a sizing guide:
http://www.qualityhats.com/stetson1.htm
6 3/4 is pretty small.