The functional properties of colloidal materials can be tailored by tuning the shape of their constituent particles. Unfortunately, a reliable, general methodology for purifying colloidal materials solely based on shape is still lacking. Here we exploit the single-particle analysis and sorting capabilities of the fluorescence-activated cell sorting (FACS) instrument, a commonly used tool in biomedical research, and demonstrate the ability to separate mixtures of synthetic microparticles based solely on their shape with high purity. We achieve this by simultaneously obtaining four independent optical scattering signals from the FACS instrument to create shape-specific 'scattering signatures' that can be used for particle classification and sorting. We demonstrate that these four-dimensional signatures can overcome the confounding effects of particle orientation on shape-based characterization. Using this strategy, robust discrimination of particles differing only slightly in shape and an efficient selection of desired shapes from mixtures comprising particles of diverse sizes and materials is demonstrated.