Modeling and controlling actuators driven by smart materials, such as shape-memory alloys (SMAs), is challenging due to their strong nonlinearities, hysteresis characteristics, and Multiphysics coupling, which limits the effectiveness of classical model-based control. This paper presents and evaluates a data-driven Q-learning controller for SMA-based actuators that learns a state-feedback policy without requiring an explicit model of the plant. The target system is a single-input, single-output, 3D-printed compliant actuator driven by SMA wires, tasked with real-time trajectory tracking. The approach bypasses system identification and controller tuning in favor of policy learning via the action-value Q-function. In real-time simulation, the learned policy reliably tracks diverse reference signals (constant, sinusoidal, square). The mean absolute tracking error ranges from 0.8 to 1.9 percent, indicating good practical accuracy even though perfect tracking is not achieved-an acceptable trade-off for many smart-material applications.