We demonstrate depth-resolved viscosity measurements within a single object using polarized optical scattering from ensembles of freely tumbling plasmon resonant gold nanorods (GNRs) monitored with polarization-sensitive optical coherence tomography. The rotational diffusion coefficient of the GNRs is shown to correlate with viscosity in molecular fluids according to the Stokes-Einstein relation. The plasmon resonant and highly anisotropic properties of GNRs are favorable for microrheological studies of nanoscale properties