Entangling a single spin to the polarization of a single incoming photon, generated by an external source, would open new paradigms in quantum optics: this relies on the possibility that a single spin induces a macroscopic rotation of a photon polarization. Up to now, however, the observed polarization rotations were limited to a few 10^-3 degrees. Here we report the amplification by three orders of magnitude of the spin-photon interaction, using a single hole spin in a quantum dot-pillar cavity system. A polarization rotation by ±6° is obtained when the spin is optically initialized in either the up or down state. We finally show how quantum measurements and quantum entanglement can be implemented with realistic cavity-QED devices.