I’m not a polygraph operator, but I know something about the job. To become a federal polygrapher, you’ll have to graduate from the basic polygraph course at the National Center for Credibility Assessment (NCCA) at Fort Jackson, South Carolina. Admission requirements for this school are listed at p. 25 of the NCCA catalog. Of note, you’ll have to have a bachelor’s degree and complete “a PDD [polygraph] examination conducted by an approved examiner.”
Before you apply, I recommend that you do some research into polygraphy and assess whether this is what you really want to do with your life. Polygraph “testing” has no scientific basis, and you will inescapably end up falsely accusing many people of lying based on your polygraph chart readings. You’ll find statements by polygraph victims here. See in particular this relatively recent statement by a former CIA analyst.
See also our free book, The Lie Behind the Lie Detector. It provides a critique of polygraph validity and policy, along with details on federal polygraph procedure and countermeasures. If, after reading it, you do decide to become a polygraph operator anyhow, your time won’t have been wasted, as it’s required reading for NCCA’s countermeasure course, which all federal polygraphers must eventually attend.