  We show how the ro-translational motion of anisotropic particles is affected
by the model of Continuous Spontaneous Localization (CSL), the most prominent
hypothetical modification of the Schr\"odinger equation restoring realism on
the macroscale. We derive the master equation describing collapse-induced
spatio-orientational decoherence, and demonstrate how it leads to linear- and
angular-momentum diffusion. Since the associated heating rates scale
differently with the CSL parameters, the latter can be determined individually
by measuring the random motion of a single levitated nanorotor.
