Earlier it was noted by the Evad3rs jailbreak team their evasi0n jailbreak tool would support iOS 6.1.2 and now it is available for download from the evasi0n website. Nothing else is new other than support for the latest version of iOS, released earlier this morning to fix the Exchange calendar bug.

Version 1.4:

Support for 6.1.2

If you are on iOS 6.1.1 and want to jailbreak iOS 6.1.2, you should first backup your Cydia tweaks (try using AptBackup to backup your tweaks prior), restore to iOS 6.1.2 in iTunes, activate and restore your iPhone, then jailbreak with evasi0n 1.4.

You can follow our video tutorial on how to jailbreak iOS 6.1 with evasi0n.

Download links for evasi0n 1.4: Mac, Windows, Linux