You join a program on edX.org simply by enrolling in any course that is part of that program -- there's no application.
Program credentials offered on edX.org
You can browse all of our available programs in the course catalog. For more information about the catalog search, please read Can you help me choose a course?
After you enroll in a course that is part of a program credential, that program on your Programs dashboard here.
Click the name of any program for more details and the option to Enroll Now in any related courses, or upgrade all remaining courses.
To complete a program you must earn a verified certificate in each of the individual courses. After you earn a verified certificate in each course, you automatically receive your program certificate.
For additional information, see How do I take all the courses in a program?