If you're referring to professional karting, stick around- someone who knows better can chime in. If you mean karting as a recreational sport- ANYTIME!
Your young'uns can learn to drive on a small kart with low gearing in large open spaces, and be tearing it up in no time! You know your kids- you should have a pretty good feel for thier capabilities. I gave my two a little lawn tractor to learn on and they did pretty well. Even so, just for safety's sake I rigged a wireless remote kill switch so I could shut it down from a distance if need be.
How old is your son?