A self-contained direction sensing radio frequency identification (RFID) reader is developed employing a dual-directional antenna for automated target acquisition and docking of a mobile robot in indoor environments. The dual-directional antenna estimates the direction of arrival (DOA) of signals from a transponder by using the ratio of the received signal strengths between two adjacent antennas. This enables the robot to continuously monitor the changes in transponder directions and ensures reliable docking guidance to the target transponder. One of the technical challenges associated with this RFID direction finding is to sustain the accuracy of the estimated DOA that varies according to environmental conditions. It is often the case that the robot loses its way to the target in a cluttered environment. To cope with this problem, the direction correction algorithm is proposed to triangulate the location of the transponder with the most recent three DOA estimates. Theoretical simulation results verify the reliability of the proposed algorithm that quantifies the potential error in the DOA estimation. Using the algorithm, we validate mobile robot docking to an RFID transponder in an office environment occupied by obstacles.