Download and install Drivers : Over Here !
Get ODIN: Over Here...
The process is meant for Galaxy S3 I9300
Enable USB debubugging and give it a good charge (though it doesnt really make an effect if off)
_First Power off device.
_after it's off, press and hold: vol.down-home-power
_then press volume up to continue
_then connect your phone to your computer via USB
_Open ODIN as Administrator
(If the phone is connected properly, one of the ID:COM boxes will turn yellow with the COM port numbe)
_Click the PDA tab in Odin and select the CF-Root-SGS3-v6.4.tar.
_In ODIN, check the Auto Reboot and F. Reset Time options. DO NOT TOUCH ANY OTHER OPTION!
_Click on the Start button in ODIN and it will start the installation process.
_Once the installation is done, the phone will restart, you can unplug the phone from the computer.
*And you should be good to go... with CWM too !
EnjoY Your rooted JB 4.1.2 SIII
Tested and verified to be working
if it doesn't work, you need to re-flash with auto reboot unchecked, then boot recovery to trigger installation
NOTE: I CANNOT TAKE RESPONSIBILITY IN CASE YOU DO SOMETHING WRONG OR SOMETHING HAPPENS FOR UNKNOW REASON OR ANYTHING !
Press Thanks if i helped !