Wie es sich trifft, bin ich wach.

English Translation

As it is, I am awake.

This is a rather odd expression, and one that I’ve not heard before. Literally “as it meets itself”. Is this common in German? It’s always hard to tell if I’m learning something that people actually say, or if this is some old expression from medieval times.

I think a good translation would be “as it so happens”.
I don’t think anyone would actually say that. Personally I have never heard anyone say it. So yes, it’s older, but not necessarily “medieval” old. People still use it in writing.

However, there is a related construction that is indeed quite common:
“Das trifft sich gut”, meaning “that is unexpected but welcome”.
Another synonymous expression is “das kommt wie gerufen”.