We demonstrate a nonintrusive technique that is capable of measuring all three-components of vorticity following small tracer particles in the flow. The vorticity is measured by resolving the instantaneous spin of the microsized spherical hydrogel particles, in which small mirrors are encapsulated. The hydrogel particles have the same density and refractive index as the working fluid-water. The trajectory of the light reflected by the spinning mirror, recorded by a single camera, is sufficient to determine the 3D rotation of the hydrogel particle, and hence the vorticity vector of the flow at the position of the particle. Compared to more conventional methods that measure vorticity by resolving velocity gradients, this technique has much higher spatial resolution. We describe the principle of the measurement, the optical setup to eliminate the effect of particle translation, the calibration procedure, and the analysis of measurement uncertainty. We validate the technique by measurements in a Taylor-Couette flow. Our technique can be used to obtain the multipoint statistics of vorticity in turbulence.