I'm a stutterer with a lovely girlfriend, so yes it's definitely possible.  The important thing is how you treat your stutter. If you stutter with confidence, show that it doesn't scare you or define you, then it isn't an obstacle. In fact it kinda looks good because a confident man is a sexy man.  But if you cower from your stutter, get all anxious and scrunched up, then that will be a turn off for a lot of girls.  I know that's far easier to say, but being confident in yourself and your stutter really is the best thing you can do. And not just for dating.