Hundreds of colleges and universities have ROTC programs on their campuses. One way to find which schools offer which ROTC programs is to go to collegeprofiles.com/rotc. Click on the ROTC branch you are interested in, whether Army, Air Force or Navy/Marines. Click on the state(s) of the school(s) you are most interested in attending.
Another website, collegetoolkit.com, allows you to compare schools. Enter "ROTC" into its search function and choose a military branch or choose "any ROTC program." There you will see schools that offer ROTC programs compared by tuition levels indicated by dollar signs, and their selectivity level, whether high, medium or low. The first two schools listed, for example, are Alabama A&M and the University of Alabama. Both have two dollar signs, which means their tuition is about the same. But the "H" next to Alabama A&M means it is highly selective in admission, whereas the University of Alabama has low selectivity.
Although many students enroll in Junior ROTC in high school and continue with the ROTC program in college, there are other ways to enroll in ROTC later. Many students do not realize they are interested in a military career until they begin college and they enroll at that time. Others enroll in ROTC after completing their first or even their second year of college. ROTC classes are electives in military science and leadership, taken along with a regular major course of study. Students who enter ROTC as juniors skip the basic class and take a summer training course instead, and then move on to the junior-level classes.
If ROTC programs are not offered at the school you would like to attend, they may be offered at nearby schools. If so, you can attend the school of your choice and simply go to the other school for your ROTC classes and activities. The website collegeprofiles.com lists affiliated schools you can attend for most of your classes, along with the nearby school that offers an ROTC program. Click on the Army icon at the bottom of the ROTC home page. Scroll down to the list of schools. The first school listed is Alabama A&M. Next to it, click on "Army ROTC crosstown affiliate schools" and you will see that you could attend Athens State University or the University of Alabama-Huntsville for most of your classes, and go to Alabama A&M for your ROTC courses.