With the progression of automotive electrification and intelligence, Steer-by-Wire technology has emerged as a pivotal factor propelling the advancement of X-by-Wire chassis technology. Nonetheless, the intrinsic mechanical traits of the mechanical transmission within the Steer-by-Wire system-such as friction, wear, aging, and jamming—significantly undermine the system's dependability, efficiency, and control performance. To mitigate these detrimental effects, this paper introduces an innovative magnetic screw integrated Steer-by-Wire system. This novel approach employs a magnetic screw to achieve the conversion between rotary and linear motion in the steering-by-wire system, thereby sidestepping the adverse outcomes associated with conventional mechanical transmission mechanisms. Subsequently, a constraint robust backstepping control algorithm converging in finite time is formulated for managing the steering angle of the integrated Steer-by-Wire system featuring the magnetic screw. The effectiveness of the proposed controller is verified through simulations conducted in Simulink.