"What century is it?"
Translation:Który mamy wiek?
"Która godzina?" is a fixed phrase. If you add "jest", I guess then "Jaka jest godzina?" is possible, although uncommon.
As for this particular sentence here, I guess "jaki mamy wiek?" makes sense as well, although in the history of mankind there are not that many centuries to choose from, it's a closed set of potential answers.
I'll change the main English translation here to say "which".