This document describes RF-Compass, a system that uses RFID tags to enable centimeter-scale localization and orientation estimation for robot object manipulation without requiring expensive motion capture systems or environmental instrumentation. It achieves this accuracy by comparing signal similarities between RFID tags placed on the robot and object to iteratively partition and refine their positions as the robot navigates. An optimization formulation jointly solves for position and orientation. Evaluation shows RF-Compass enables effective robot navigation in non-line-of-sight scenarios and achieves localization accuracy within a few centimeters and degrees. This opens opportunities for mobile robot manipulation using low-cost RFID tags.