We demonstrate trapping and rotation of two mesoscopic particles in vacuum using a spatial-light-modulator-based approach to trap more than one particle, induce controlled rotation of individual particles, and mediate interparticle separation. By trapping and rotating two vaterite particles, we observe intensity modulation of the scattered light at the sum and difference frequencies with respect to the individual rotation rates. This first demonstration of optical interference between two microparticles in vacuum leads to a platform to potentially explore optical binding and quantum friction effects.