Unmanned manipulator-equipped satellite could perform on-orbit servicing mission or could be used to remove large space debris from orbit. Planning a manipulator trajectory that will lead to a safe capture of a selected grasping point on the target object is a challenging task, as the satellite-manipulator system is in a free-floating state. Moreover, complicated structure of the target satellite (e.g., arrays of solar panels) results in obstacles that must be avoided by the satellite-manipulator system. In this paper we present application of Rapidly-exploring Random Trees (RRT) algorithm for trajectory planning of such system. This algorithm proved to be well suited for a considered case, as state of the satellite-manipulator system is highly dimensional (12 + 2n dimensions) and various constraints must be taken into account (e.g., joint limits and obstacles). Operation of the RRT algorithm is successfully demonstrated in a simplified simulation example.