I'm 6'3" and have ridden everything from a 58cm to a 62cm. Current bike is a 61cm but that's a compact frame. Just goes to show how sizes vary between brands. Traditional frames (ie horizontal top tube) are relatively rare these days, most companies go for compact or semi-compact geometry.
It's not the seat-tube length that's the issue particularly, more the top tube and hence the reach.
The only way to find out is to go to a decent roadie shop and try a few. I'd be guessing you need a 60cm minimum and you might find those hard to come by in bike shops, maybe try a shop with a bike-fitting/measuring jig.