A novel Monte Carlo-based indoor radio-frequency identification (RFID) positioning scheme is proposed for dual-antenna RFID systems with the cooperation of dual-antenna joint rectification. By deploying reference passive RFID tags on the ground to establish an RFID tag-based map, indoor self-positioning of a moving platform carrying an RFID reader with two forward-looking antennas can be simply implemented by looking up the positions of responded RFID tags at each time step of movement, and estimating the platform position by using the proposed Monte Carlo-based algorithm. To improve the positioning accuracy of Monte Carlo-based positioning, each antenna channel, with its own footprint on the ground, may rectify its position estimation by using the tag position information interrogated by the other antenna channel. The algorithm for dual-antenna rectification is proposed. The performance of the proposed Monte Carlo-based self-positioning scheme is demonstrated by both simulation and experiment tests. Some factors in a practical indoor-positioning system, such as the reference tag distribution pattern, reader antenna footprint size, and footprint overlap, are discussed. Some guide rules for deploying the RFID indoor-positioning system are also reported.