She is probably over 30 years old, but the timeline isn't very specific.
The League was started about 22 years ago in Runeterra time, which seems to flow at the same speed as Earth time.
Katarina was one of the first champions to join the League, but it's difficult to pinpoint when she did join exactly. Noxus was definitely part of the League before 10 CLE (10 years after the League was created), and Katarina was part of it back then. So count 12 years after that, combined with the idea that she probably didn't join before age 18, and voila. At least 30 years old.
Now, what that age actually means hasn't really been talked about. People in Runeterra could age differently, so you can't really compare it to 'our' 30-year-olds at the moment. In the end, it's up to your imagination.