The correct term would be "its your turn" for most uses. " I've had my turn. Now it's your turn" "it's your time" would be used sometimes in a different context "it's your time to take over now"

now is your time to shine my time was then, your time is now i went first, now it is your turn

Your turn is it, when it is your time to do something. A simple phrase to remember the difference. :) A turn is an opportunity to do something.