As long as a tire steers about a titled kingpin pivot, the point coming in contact with the road moves along its perimeter. This movement affects the determination of kingpin moments caused by the tire forces, especially for large steering angles. The movement, however, has been neglected in the literature on the steerable-tire-kinematics-related topics. In this investigation, the homogeneous transformation is employed to develop a kinematic model of a steering tire in which the instantaneous ground-contact point on the tire is considered. The moments about the kingpin axis caused by tire forces are then computed based on the kinematics. A four-wheel-car model is constructed for determining the kingpin moment of steering system during the low-speed cornering maneuver. The result shows that the displacement of the ground-contact point along the tire perimeter is significant for large steering angles. It also indicates that, at the low-speed cornering, the moment about the kingpin axis caused by vertical forces benefits self-centering while those caused by longitudinal forces, lateral forces, and ‘aligning’ torques facilitate the turn. A parameter study is also conducted to visualize the effects of wheel alignment parameters on the kingpin moment. It appears that an increase in kingpin offset or a decrease in caster angle affects the kingpin moment such that it supports the self-centering. The effects of kingpin inclination and caster trail on the moment, however, depend on the amplitude of steering angle. The result is compared to those derived from a multi-body model for validation.