Absolutely, it comes from the children's game of "tag."
I use it when we get caught up in a game of "telephone tag" in which we repeatedly leave voicemails for the other person, never catching that person at their desk. After this happens a couple times, instead of saying "Hi, this is Barb, returning your call that returned my call when I left you that message..." I will just say "Hey, it's Barb again. Tag, you're it." And then it's that person's role to try to call me again... etc.