This method was published by invisibleK of RootzWiki and is tested on Samsung Galaxy SIII SCH-I535 from Verizon Wireless. This method only roots the phone for you. It does not install ClockWorkMod recovery or a custom ROM.
Steps to jailbreak Verizon Galaxy SIII
1. Download the USB drivers here.
2. Download ODIN v3.07 from the link at the end of this post.
3. Download the rooted system.img here.
4. Install the Samsung Verizon SIII drivers you downloaded in step 1, on your computer.
5. Switch off your phone and switch it on by pressing [Volume DOWN] + [Home] + [Power]. Keep pressing till a warning message appears. Now press [Volume UP]. A green Android will show up on the screen with a message saying “Downloading” .
6. Connect your phone to the computer and launch ODIN
7. Once ODIN is running, go to the PDA section and select the file you downloaded in step 3 and click Flash.
8. It will take anywhere from 10 to 20 minutes for the process to complete.
9. Now your phone will reboot. Once booting completes, disconnect your phone from the computer.
10. Congratulations your phone is now rooted.