The exact requirements for joining the ROTC program vary a bit by branch of service, but generally, students must be accepted to or enrolled at a college approved by the ROTC program. The process starts by speaking to a military recruiter.
ROTC involves taking some additional classes on top of a normal college schedule, so the college the student is attending must offer ROTC classes. Each branch of service has certain approved colleges for its program, so the process of joining ROTC usually begins while the student is still in high school.
Students who are already enrolled at a ROTC college can still join the program provided they are not too close to graduation and meet the program's age requirements. The services usually require the student be no older than 27 by the time they graduate and get their commission, but this can be adjusted upward in some branches if the student has prior military experience.
Enlisted members of the Army may be able to join the ROTC program through the "Green to Gold" scholarship program.
General requirements for all ROTC programs are that the applicant be a U.S. citizen or in the process of becoming naturalized, and participants must be medically qualified by the branch of service that they are joining.