I suggest you use Chainfire's CF Autoroot, which is straightforward and uses the Odin method to root your device. Get the file from here
CF-Auto-Root and select the correct device (GT-i9300T) and go the one but last cell of the row in the table then click on File and download. After downloading extract the .zip and copy the .tar.md5 file to a folder of your choice. then start Odin and flash the file in the usual manner (PDA > locate file > choose the .tar.md5 downloaded > Start).