A fault tolerant control for vehicle Steer-by-Wire (SbW) systems in the presence of actuator fault and bounded uncertainties is proposed. The minimax model predictive control (MPC) in the delta-domain is exploited to achieve the tracking performance under actuator fault, system uncertainties and disturbance. The feedback control action based on estimation error in parallel with the minimax MPC controller, ensures the system's robust asymptotic stability in the presence of estimation errors. A fault observer is developed to estimate both the fault information and the faulty SbW system. Both simulation and experimental results demonstrate that the proposed fault tolerant control strategy can handle various types of actuator faults. It has better robustness to system uncertainties and estimation errors compared to shift-operator based MPC controller and PD controller, and maintains superior steering performance.