Robust image hashing, which maps the perceptual contents of image to a short digest, is a key technique for tackling the challenges of content-based indexing, searching and copyright protection. In this letter, we propose a quaternion invariance based hashing algorithm that can fuse complementary visual features to compact hash. The proposed algorithm leverages quaternion polar cosine transform to holistically capture the spatial and chromatic characteristics of digital image, and rotation-invariant features are derived from the phase information in the quaternion frequency domain. In addition, we also propose an information theoretic based metric for feature quality assessment and a greedy strategy to select the optimal subset of features for hash computation. Extensive experiments over a large database demonstrate that the proposed work shows higher content identification accuracy than most competing algorithms, and the resulting hash is compact and easy to compute.