See if you wanna go for the course of BCA then also you will learn Full Stack as your Discipline Specific Elective subject which you may select. If you are in a good university, you will get a basis of your education to be of good class and the teachers and alumni network will make your learning process fluent. Now if you want to go for the BCA Full Stack you can go for it but what happens is, the student thinks they like a specialization but when they study they may loose interest as a result they can coup up. SO if you are 100% sure about your interest in Full Stack then only go for it. But if you don't have any proper exposure to the subject and you just read or heard something about the Full Stack, then I would recommend you to keep a open space for your education which you will get from the BCA. So you have to judge your condition and decide accordingly.

To know more about BCA, visit the link below:

https://www.careers360.com/courses/bca-bachelor-of-computer-applications

I hope this answer helps. All the very best for your future endeavors!