Developing automatic driving solutions and driver support systems requires accurate vehicle specific models to describe and predict the associated motion dynamics of the vehicle. Despite of the mature understanding of ideal vehicle dynamics, which are inherently nonlinear, modern cars are equipped with a wide array of digital and mechatronic components that are difficult to model. Furthermore, due to manufacturing, each car has its personal motion characteristics which change over time. Hence, it is important to develop data-driven modelling methods that are capable to capture from data all relevant aspects of vehicle dynamics in a model that is directly utilisable for control. In this paper, we show how Linear Parameter-Varying (LPV) modelling and system identification can be applied to reliably capture personalised model of the steering system of an autonomous car based on measured data. Compared to other nonlinear identification techniques, the obtained LPV model is directly utilisable for powerful controller synthesis methods of the LPV framework.