Membership in a ARMS affiliated club is also required for road racing competition. Most of the race organizing clubs have a majority of members involved in racing themselves, and will gladly answer your questions. Your club remains a valuable source of support, information and advice. Here is a list of links to the local clubs involved with road racing (makes sense to join the one you live closest to):
You must successfully complete an authorized racing school as described before. Proof of graduation, a completed ARMS licence application, a physical examination and medical form completed and signed by your doctor, and your club membership information must then be mailed in, along with the licence fee. These applications and forms can be found on this HERE. Cost is $120.
UPDATE: if you are a racer in another series (like Oval Track racing), you can make a request to the Race Director to obtain a licence without having to take a school. This will be dealt with on a case by case basis.