Absolutely you should be able to get a job!! Believe it or not I have managed to land a job in my field of psychology, talking to people all day every day and even delivering training, and while my stutter is obviously present I've still managed to make it work pretty well. Some commenters here have suggested mentioning your stutter during the interview process- I generally do that too, however usually in person before the interview starts. Just so they don't think I'm "so anxious I can't speak" or anything. Having a stammer sucks but it's part of me and I'm done letting it hold me back. I understand that this is far easier said than done but I really am wishing you all the luck in the world, my inbox is always open if you ever fancy a chat or just a box to rant into. Good luck!!