Mention it in your cover letter when you apply and pass it off as a strength, not a weakness--show what you, from your experiences with your stammer understand about using web development to communicate with users that other developers just wouldn't naturally understand.

Then, when you go get invited for an interview, make sure you control the variables of the situation beforehand: remind the person who schedules the interview that you have a stammer and ask if you can bring a tablet computer to use to help communicating with the interviewer (or something similar that would work). If you set the rules for how the interview proceeds beforehand, it should give you control of the situation and show that you are in control of being able to communicate and work successfully despite the stammer.