This paper proposes an automatic registration method for optical and Synthetic Aperture Radar (SAR) images based on geometric structural properties. In the proposed method, the phase congruency feature with photometric invariance is first introduced for image feature extraction, and then both the magnitude and orientation information of phase congruency are used to build a geometric structural feature descriptor named HOPC (Histogram of Orientated Phase Congruency). A similarity metric named HOPCn is defined for image matching by using the Euclidean distance of the descriptors. This similarity metric can capture the geometric structural similarity between images, and has been tested using 4 pairs of optical and SAR images. Experimental results show that HOPCn is robust to non-linear radiometric differences, and outperforms the state-of-the-art similarity metrics such as correlation coefficient and mutual information. Moreover, this paper also design an automatic registration method based on HOPCn. Experimental results demonstrate the effectiveness and robustness of the proposed method.