This paper details a concurrent attitude and orbit control method for a debris-removing nanosatellite, called deobriter CubeSat, during the rendezvous and synchronization maneuver with an uncontrollable tumbling debris object. The CubeSat is designed based on the utilization of an eight-unit form factor and commercially-available components with substantial space heritage, and is intended for the removal of sizable debris objects in low-Earth orbit. In particular, a low-thrust propulsion system is used for orbit control, as well as three reaction wheels allowing for a three-axis attitude control. Since the thruster can only produce force in one direction in the body frame, the spacecraft is considered to be underactuated. The controller employs the reaction wheels and the thruster to simultaneously rendezvous and synchronize the attitude of the CubeSat with the tumbling debris object, allowing for a concurrent attitude and position tracking. Detailed derivation of the concurrent controller is discussed, the effects of high-order derivatives are analyzed, and the stability of the system is proved. Simulation scenarios are created for two different thruster operation modes, namely, unsaturated thrust force and continuously-saturated thrust force, in order to verify the performance of the controller, as well as its robustness against gravity gradient disturbance torque and gravitational perturbation force.