Path tracking control is a critical function for autonomous vehicles. However, the inevitable response delay of the steering actuator deteriorates tracking accuracy and overall stability—effects that become pronounced when the curvature of the reference path changes rapidly, leading to performance deterioration and oscillations. To resolve the actuator delay issue identified on an experimental platform, this paper proposes an effective path tracking control strategy to ensure precise and stable vehicle navigation. Specifically, a pure delay and first-order inertial lag are incorporated into the vehicle model and augmented as additional states within the tracking error framework, thereby explicitly compensating the steering delay. The lateral control algorithm is designed using Model Predictive Control (MPC) and evaluated through Simulink–CarSim co-simulation tests under small-curvature overtaking (double-lane-change) and serpentine manoeuvres. Simulation results indicate that the proposed delay-compensated control algorithm significantly reduces the maximum lateral error by 40.7% and 43.3% in these two manoeuvres, respectively, while preserving high accuracy and favourable stability. Furthermore, full-scale vehicle tests conducted on a drive-by-wire chassis demonstrate that, compared to a baseline controller ignoring actuator delay, the proposed strategy reduces the maximum lateral error by 26.4% in a single-lane-change scenario, confirming the effectiveness and robustness of the proposed method.