Introducere.

Eu sunt student universitar.

I'd rather say :

Eu sunt student la universitate.

or just
Eu sunt student.

In Romanian the word "elev" (fem. "elevă") is used for primary school, gymnasium, highschool.

And "student" (fem. "studentă")  is used for university, college.

So when you say "eu sunt student"  anyone will understand that you are studying in an university or college.   "student universitar" sounds redundant.

However the word "universitar" is suitable when talking about teachers:  "profesor universitar".  I think that in English you use just "professor" in this case.   

Introducere.

Bună! Ma numesc Mike. Sunt din America. Eu sunt student universitar. Îmi place romăna dar este grea. Mulţumesc pentru citit! La revedere.