Rooting a Samsung device almost always has the same procedure for almost every Samsung device, which involves a simple flash of a rooted stock kernel using the flashing utility Odin (which is also used to flash firmware, kernels, etc.), and the same method is also used to root the Verizon Galaxy S3, though thanks to the locked bootloader on the Verizon variant, one needs to flash a full rooted stock firmware which clocks in at around 800MB-1GB as flashing kernels on a locked bootloader is not possible.
So for those who would prefer not having to download such a big file in order to root, XDA Senior Member Noxious Ninja has come up with GS3DebugFSRoot, a tool for rooting the Verizon Galaxy S3 without the need to flash a full firmware using Odin. Using GS3DebugFSRoot is quite simple. Simply connect phone to computer with USB debugging and watch it work its magic to give you a rooted phone. Now, Odin is a completely safe and convenient method for rooting, but it’s nice to have a tool that does the job so much quicker and without the need to download a huge file just to gain root access, all because Verizon so cruelly decided to lock the bootloader on the Galaxy S3.
Head over to the official development page on XDA to download GS3DebugFSRoot and for clear and detailed instructions on how it can be used to root your Verizon Galaxy S3. Try it out and drop a line in the comments to let us know how it works for you. Happy rooting!