This paper presents a discrete adaptive super-twisting sliding-mode controller for steering-angle tracking in a steer-by-wire actuator. A lumped-disturbance observer estimates the combined effect of friction, external torque, parameter variation, and unmodeled dynamics. Projected gain adaptation is used to adjust the switching intensity within a prescribed range, and a 15 ms CAN delay is included in the command path. The controller is compared with PID and fixed-gain super-twisting control in simulation. For a 0.8 rad reference and a 3 N m disturbance introduced at 0.6 s, the PID response loses tracking, while the proposed method restores tracking with lower visible oscillation than the fixed-gain super-twisting controller. The disturbance estimate approaches the imposed disturbance after its step change.