The idea of intelligent tires is to develop a tire into an active perception component or a force sensor with an embedded microsensor, such as an accelerometer. A tire rolling kinematics model is necessary to link the acceleration measured with the tire body elastic deformation, based on which the tire forces can be identified. Although intelligent tires have attracted wide interest in recent years, a theoretical model for the rolling kinematics of acceleration fields is still lacking. Therefore, this paper focuses on an explicit formulation for the tire rolling kinematics of acceleration, thereby providing a foundation for the force identification algorithms for an accelerometer-based intelligent tire. The Lagrange–Euler method is used to describe the acceleration field and contact deformation of rolling contact structures. Then, the three-axis acceleration vectors can be expressed by coupling rigid body motion and elastic deformation. To obtain an analytical expression of the full tire deformation, a three-dimensional tire ring model is solved with the tire–road deformation as boundary conditions. After parameterizing the ring model for a radial tire, the developed method is applied and validated by comparing the calculated three-axis accelerations with those measured by the accelerometer. Based on the features of acceleration, especially the distinct peak values corresponding to the tire leading and trailing edges, an intelligent tire identification algorithm is established to predict the tire–road contact length and tire vertical load. A simulation and experiments are conducted to verify the accuracy of the estimation algorithm, the results of which demonstrate good agreement. The proposed model provides a solid theoretical foundation for an acceleration-based intelligent tire.