The jailbreaking community can sometimes be a fast or slow one at getting new jailbreaks out when Apple releases a new update, but it seems the MuscleNerd, who is part of the iPhone Dev team has already found a way to jailbreak iOS 6 Beta, don’t get to excited as not all of it works:
Here's ioreg of my tethered-JB ipt4g 6.0: http://t.co/50LBbsGD ..MANY things including Cydia are broken, don't expect beta JB for a while!
— ? MuscleNerd (@MuscleNerd) June 12, 2012
But you can probably expect a full and working version of the jailbreak pretty soon, but of course as soon as iOS 6 is released they will have to do it all over again.