Link: CWM Recovery for all
Instructions for CWM recovery to enable rooting and customization of all SGS3 LTE variants. This is confirmed to work great on Sprint, AT&T, T-Mobile and Rogers variants.
Link: Root from Recovery
Simply flash this.zip in CWM and your phone is rooted! This is the easiest method to root the stock Samsung ROM.
Follow these insructions to unroot and restore the modification status to "Normal".