I think that the existing answers have a good handle on giving advice about how to do it. In particular, it seems Twitter for a specific purpose within a course is a much better idea than using it for general communication. If nothing else, it seems unprofessional to me to communicate via twitter unless something about the course is specifically twitter or social media centric.
To add a personal anecdote, as a student at Georgia Tech I was told that a student-created Slack wasn’t an official channel for communication but that a professor-created Slack could be. The concern was about potential FERPA violations, though no specifics were given.
I am not a lawyer. That said, it doesn’t seem to be an issue with FERPA to me. The status of digital communications doesn’t seem to have been addressed much in US case law, with two relevant cases that I could find.
Owasso Independent School Dist. No. I-011 v. Falvo (argued before SCOTUS) seems to imply that there is reason to believe that electronic communications aren’t “student records” as defined by FERPA, for the same reason that the records in that case aren’t: they aren’t maintained or kept by the teacher or the school. The one court case on this specific issue seems to take this same approach. * S.A. v. Tulare County Office of Education, 2009*, found that
Emails, like assignments passed through the hands of students, have a fleeting nature. An email may be sent, received, read, and deleted within moments. As such, Student’s assertion – that all emails that identify Student, whether in individual inboxes or the retrievable electronic database, are maintained ‘in the same way the registrar maintains a student’s folder in a permanent file’ – is ‘fanciful.’ Like individual assignments that are handled by many student graders, emails may appear in the inboxes of many individuals at the educational institution. FERPA does not contemplate that education records are maintained in numerous places. As [SCOTUS] set forth . . . ‘Congress contemplated that education records would be kept in one place with a single record of access.’”
So, I’m inclined to think that digital records aren’t intrinsically problematic. That said, there are many issues at play including institutional policies and you shouldn’t do this without talking to your university lawyers first.