Watermarking of digital images is a well-known technique that is widely used for securing image contents. A successful watermarking method must be accurate, reversible, resilient, and robust against various attacks. In this paper, we propose a reversible and robust color image watermarking method. A new set of multi-channel fractional-order polar harmonic transforms and their geometric invariants have been derived. These highly accurate and geometrically invariant features are used in the watermarking process. The binary watermark’s bits were scrambled using a 1D chaotic sine map to increase the security level. A set of experiments were performed to evaluate the proposed watermarking method, and its performance was compared with recent color image watermarking methods having similar colors. The obtained results showed high visual imperceptibility and superior robustness against geometric and signal processing attacks.