This paper presents an autonomous navigation system for a mobile robot using randomly distributed passive RFID tags. In the case of randomly distributed RFID tags, it is difficult to provide the precise location of the robot especially in the area of sparse RFID tag distribution. This, combined with the wide turning radius of the robot, can cause the robot to enter a zigzag exploration path and miss the goal. In RFID-based navigation, the key is to reduce both the number of RFID tags and the localization error for practical use in a large space. To cope with these, we utilized the Read time, which measures the reading time of each RFID tag. With this, we could estimate accurately the localization and orientation without using any external sensors or increasing the RFID tags. The average estimation errors of 7.8 cm in localization and 11 degrees in orientation were achieved with 102 RFID tags in the area of 4.2 m by 6.2 m. Our proposed method is verified with the path trajectories produced during navigation compared with conventional approaches.