Generally speaking, the answer is yes, most Catholic universities require students to take some religious courses as part of their academic journey. Because Catholic Universities are so committed to creating a likeness to Christ in each of their students and preparing them to serve and love their future communities as He would, requiring students to take religious courses is very common. In order for them to be more like Christ, they need to know Him and learn about him.
The question between Catholic Universities is not so much if they will require religious courses as how many religious courses students will be required to take. The answer to that varies by school and by academic track/major. Be sure to check with the admissions department or an academic advisor of the school you want to go to for their requirements.