Automotive self-localization is an essential task for any automated driving function. This means that the vehicle has to reliably know its position and orientation with an accuracy of a few centimeters and degrees, respectively. This paper presents a radar-based approach to self-localization, which exploits fully polarimetric scattering information for robust landmark detection. The proposed method requires no input from sensors other than radar during localization for a given map. By association of landmark observations with map landmarks, the vehicle's position is inferred. Abstract point- and line-shaped landmarks allow for compact map sizes and, in combination with the factor graph formulation used, for an efficient implementation. Evaluation of extensive real-world experiments in diverse environments shows a promising overall localization performance of $0.12 \text{m}$ RMS absolute trajectory and $0.43 {}^\circ$ RMS heading error by leveraging the polarimetric information. A comparison of the performance of different levels of polarimetric information proves the advantage in challenging scenarios.