There are. The two main regulations to keep in mind when it comes to privacy and texting are the Family Educational Rights and Privacy Act (FERPA) and the Telephone Consumer Protection Act (TCPA).
The FERPA act simply states that a student's information should be kept private. In other words, only those who have a legitimate need to see the student’s data should be able to. FERPA regulations do not apply to prospective students.
TCPA laws are much broader. They are not specific to education and apply to everyone, whether they're current students, parents, alumni or even prospective students. It's also a best practice keep all regulations currently in place for phone call and email communications and apply them to all texting communications as well.
You can read more about these laws here.