The steering trapezoid designed according to the Ackermann steering geometry potentially causes excessive tire wear and affects the steering performance due to the large tire deformation resulting from large lateral acceleration. To address these problems, this article introduces a design method for a race car steering system that considers the tire side slip angles to optimize the target steering angle relation. First, a racing path was planned by genetic algorithm according to the given race track and race car driver characteristics. Next, the objective function of the ideal steering angle relation was constructed by introducing the Ackermann correction coefficient and establishing the modified Ackermann steering geometry model, considering the tire side slip angle. Then, a data acquisition experiment was designed, and the Ackermann correction coefficient was identified by the proposed simulation algorithm. Finally, the coincidence degree of wheel steering centers was defined as the evaluation index, which can be used to describe and evaluate the performance of the coordination for wheels’ movement. Simulation results show that the design method of the steering system effectively improves the handling stability of the race car and reduces the tire leaning-grind.