“Je comprends” has the same meaning, but is in my opinion somewhat more formal than “got it”. If you want to keep the general tone, “Compris” might be a better translation.

C’est compris keeps the familiar tone of got it. Likewise, it can be used both as an assertion and as an interrogative.

You might hear “Pigé !” for “Got it !” in informal situations.

People in France will also say ‘ok!’, English has really permeated the country by now.
But you can say ‘compris!’ as well, or ‘d’accord’ if you are agreeing on statement.

Got it! is incorrect in English and as said above means “j’ai compris”. Now you may want to keep the meaning and the incorrectness, for instance in a translation of a book. Then Pigé ! is excellent.