Gabriel1 is correct there is not an untethered jailbreak for that version and Probably won't ever be one. I'm sure once apple comes out with another major ios version there will be a new jail break. I could be incorrect however I thought I heard something about a semi untethered jailbreak for iOS 6.1.3. This means every time you want to reboot your phone you would have to plug it in to a computer. And if you are not near a computer you would be able to your phone but all the jailbreak tweaks and apps would not be available. However I would not recommend this I would wait until the next iOS comes out and they jailbreak it. Remember after six came out it was only a few days before it was jailbroken. I lucked out i did upgrade my phone however i had an issue with the speaker and sent it back and the new one i got was on iOS 6.1.2. If I was you I would just patiently wait until a new jailbreak is released. I hope I helped good luck.