Hold down Volume Down, Home Center, and Power buttons together for about 20 seconds until your phone resets and shows you an option to get into download mode.
Next hit Volume Up button to enter download mode.
Once in Download mode, you can connect your micro-USB cable from your Galaxy S3 to your computer.
Next, download GalaxyS3Root.zip and unzip
Next, make sure you have drivers installed, you should see “Samsung Mobile USB CDC Composite Device” in Device Manager. If you don’t, simply download Samsung Kies and install it. (Then unplug, plug the micro-USB cable.)
Double-click on odin3 v1.85.exe file to start ODIN. You should see a yellow highlighted box with a COM number. The number doesn’t matter just so long as you see a yellow box. If you don’t see yellow box, your drivers are not installed correctly OR try killing Kies in Task Manager as sometimes it can interfere.
Choose “PDA” and choose “CF-Root-SGS3-v6.1.tar” file in GalaxyS3Root folder. Then hit “Start”.
In about 10 seconds, your phone will reboot and give you ClockworkMod Recovery and full root.
You will get a “PASS!” if everything went correctly.
Your phone will automatically reboot into ClockworkMod Recovery and install root/Superuser files.
Once your phone reboots, you will find “SuperSU” app, which is the Superuser app.
You can verify you have root by running a rooted app such as Titanium Backup app, you will see Superuser request window pop up. Hit “Grant” everytime you see this.
You can now get into ClockworkMod Recovery anytime by holding down Volume Up, Center Home, and Power button together for 20 seconds.
NOTE:I'm not responsible if you mess up your phone. Make sure you know what you are doing before following any instructions. Go here .Just read it.