Spintronics relies on the ability to transport and use the spin properties of an electron rather than its charge. We describe a spin ratchet at the single-electron level that produces spin currents with no net bias or charge transport. Our device is based on the ground-state energetics of a single-electron transistor comprising a superconducting island connected to normal leads via tunnel barriers with different resistances that break spatial symmetry. We demonstrate spin transport and quantify the spin ratchet efficiency by using ferromagnetic leads with known spin polarization. Our results are modeled theoretically and provide a robust route to the generation and manipulation of pure spin currents.