This paper presents the localization of a mobile robot while simultaneously mapping the position of the nodes of a Wireless Sensor Network using only range measurements. The robot can estimate the distance to nearby nodes of the Wireless Sensor Network by measuring the Received Signal Strength Indicator (RSSI) of the received radio messages. The RSSI measure is very noisy, especially in an indoor environment due to interference and reflections of the radio signals. We adopted an Extended Kalman Filter SLAM algorithm to integrate RSSI measurements from the different nodes over time, while the robot moves in the environment. A simple pre-processing filter helps in reducing the RSSI variations due to interference and reflections. Successful experiments are reported in which an average localization error less than 1 m is obtained when the SLAM algorithm has no a priori knowledge on the wireless node positions, while a localization error less than 0.5 m can be achieved when the position of the node is initialized close to the their actual position. These results are obtained using a generic path loss model for the transmission channel. Moreover, no internode communication is necessary in the WSN. This can save energy and enables to apply the proposed system also to fully disconnected networks.