I believe I read a scholarly article that stated violence in video games has no correlation whatsoever with real life violence, meaning that those exposed to violent video games will not necessarily become violent people themselves.
I started playing GTA San Andreas when I was in elementary school, probably around grade 5, and here I am today. To be honest I think it would really depend on the child that you're giving the game to, as in, whether or not they'd mimic what they see in video games and TV in real life. Obviously, if a child can't differentiate between socially acceptable and socially incorrect behaviour, then they shouldn't be playing games like GTA. If I was a parent, I definitely wouldn't let my child play it until the final years of elementary school (same time as me, grade 5 to 6-ish). But by that time, I'm pretty sure the child would have some sense of morality and socially acceptable acts, so it wouldn't be a problem at all.