We have prepared monodisperse suspensions of nematic liquid crystal droplets in water. The droplets are stabilized by polyvinyl alcohol, a polymer that induces planar anchoring of the liquid crystal molecules at the surface of the droplets. The resultant particles exhibit strong optical anisotropy while having a spherical shape. As a consequence, the light scattering from the particles contains a strong depolarized component. We report a simple application of this feature by performing dynamic light scattering experiments to measure the rotational diffusion of colloidal spheres in a dilute suspension.