Can I ever get a job in communications with a stutter?

Can I ever get a job in communications with a stutter? My stutter is getting to the point where it's getting me down, and I don't think I can take it anymore. This afternoon, I got a rejection email today from a PR company I interviewed with last Friday where I stuttered on interview questions even though I was perfect for it. Today, I also had an interview for an advertising agency where I had to do a two-minute presentation and embarrassingly stuttered my way through to the end in front of the entire room, even though everyone else was fluent, so I'm sure that is another rejection. My stutter is mostly anxiety induced, which gets me in presentations and interviews, so what I want to know from fellow stutterers is if anyone who stutters, mildly or severely, has worked in communications successfully before? Maybe it's not that, but every time I get a rejection, I feel like it's down to the stutter and it makes me feel like I'm worthless, even though I have the CV to back it up. I'm fine outside of interviews, but that's the only time they'll see me, so if I stutter there, should I even bother pursuing a career in PR/comms?