Mobile Mapping Systems (MMS) can be defined as moving platforms which integrates a set of imaging sensors and a position and orientation system (POS) for the collection of geo-spatial information. In order to fully explore the potential accuracy of such systems and guarantee accurate multi-sensor integration, a careful system calibration must be carried out. System calibration involves individual sensor calibration as well as the estimation of the inter-sensor geometric relationship. This paper tackles a specific component of the system calibration process of a multi-camera MMS the estimation of the relative orientation parameters among the cameras, i.e., the inter-camera geometric relationship (lever-arm offsets and boresight angles among the cameras). For that purpose, a novel single step procedure, which is easy to implement and not computationally intensive, will be introduced. The proposed method is implemented in such a way that it can also be used for the estimation of the mounting parameters among the cameras and the IMU body frame, in case of directly georeferenced systems. The performance of the proposed method is evaluated through experimental results using simulated data. A comparative analysis between the proposed single-step and the two-step, which makes use of the traditional bundle adjustment procedure, is demonstrated.