This work addresses the position tracking control problem for tendon-driven robotic mechanisms in the presence of parametric uncertainty and additive external disturbances. Specifically, a full state feedback nonlinear robust controller is proposed to tackle the link position tracking problem for tendon-driven robot manipulators with uncertain dynamical system parameters. A robust backstepping approach has been utilized to achieve uniformly ultimately bounded tracking performance despite the lack of exact knowledge of the dynamical parameters and presence of additive but bounded disturbance terms. Stability of the overall system is proven via Lyapunov based arguments. Simulation studies performed on a two link planar robot manipulator driven by a six tendon mechanism are presented to illustrate the effectiveness and viability of the proposed approach.