This article applies a singular perturbation theory to solve an optimal linear quadratic tracker problem for a continuous-time two-time-scale process. Previously, singular perturbation was applied for system regulation. It is shown that the two-time-scale tracking problem can be separated into a linear-quadratic tracker (LQT) problem for the slow system and a linear-quadratic regulator (LQR) problem for the fast system. We prove that the solutions to these two reduced-order control problems can approximate the LQT solution of the original control problem. The reduced-order slow LQT and fast LQR control problems are solved by off-policy integral reinforcement learning (IRL) using only measured data from the system. To test the effectiveness of the proposed method, we use an industrial thickening process as a simulation example and compare our method to a method with the known system model and a method without time-scale separation.