I have a Bachelor of Arts degree in English and I've been in IT for almost 27 years. When I was in college, there were no Computer Science degrees offered. In fact, I don't recall there even being a computer science course offered, much less a possible degree.

I work with one programmer that has a Bachelor of Science in Accounting, and other with a degree in Music. It is easier to get into programming with a programming degree, but it is not essential. If you don't have a degree in programming, you will have to work a lot harder to get your foot in the door than would someone with such a degree, but it is still possible.