Dating your college professor illegal
So, unless your school has a specific policy on the subject, it's probably ethical, as long as you make sure to avoid being in a position that creates a specific conflict.
You should check your school's HR handbook or department policy. If you don't violate their rules, and the relationship is mutually agreeable, best of luck to you both.
However, many of the instructors at your school are barely scraping by.
And in those moments, we certainly haven’t given a hoot what the person behind the podium thinks.