What kind of job do you want to apply for? Job in the field or behind a desk? Most jobs in intelligence services are the latter, and I don’t really see an issue in applying with a stutter (even if it’s severe) as long as you have a good degree in a field like computer science, law, political science, criminology. If you plan on becoming an FBI field agent it might pose a problem (in my country stuttering can be an exclusion-criterion for the police force) but I would still try to apply.