Is it ethical for a college professor to adopt a student?

It's unclear whether you mean legal or figurative adoption. Either way, it seems it would be ethical if 1) the student needed or benefited from the adoption and 2) the realtionship is healthy and balanced. Whether literal or figurative, if the student is provided mentoring, positive influence and further education, and further is not exposed to an inappropriate physical relationship, then the relationship can be very beneficial.