Would requiring students to use Twitter as an integral part of a course potentially conflict with FERPA?
To elaborate on @Danny Ruijters comment:

The acceptableness of using Twitter as a course requirement greatly depends on the course itself and how Twitter will be used. Courses which could easily integrate Twitter are business courses focusing on topics such as:


Marketing
SEO (Search Engine Optimization) 
SMO (Social Media Optimization)
SMM (Social Media Management)


If a course wanted to use Twitter as a form of communication (could be an argument to make with a business communications course depending on the syllabus) then there's no reason to use Twitter. I don't know a single school that doesn't have a student email system and more and more schools have online learning centers used by both virtual and ground (in class) courses. 

In a case where Twitter was acceptable students should NOT be forced to use their own personal accounts or even release the name of their personal account.