Robot trajectory tracking control based on differential-algebraic equation (DAE) models is still a thorny issue, because the DAEs of such systems are inherently complex and unstable, such as the high-index problem. In this paper, a symplectic instantaneous optimal control (IOC) method for robot trajectory tracking with input saturation based on controlled DAEs is proposed. Based on the discrete variational principle and the canonical transformation, a symplectic discretization form for the controlled DAEs is first constructed. Then, the continuous trajectory tracking problem is approximated for a series of IOC problems at every time step, and the linear complementarity problem (LCP) can be derived for solving the IOC problems. Finally, the control inputs can be obtained by solving the corresponding standard LCP. The proposed method provides a unified framework for solving the trajectory tracking control problems of robot multibody dynamic systems. Numerical simulations and virtual experiments are conducted to verify the robustness and the efficiency of the proposed method, i.e., the input saturation constraints are satisfied at the discrete time points, and high accuracy tracking control results can be obtained at low computational cost.