We report a picosecond time-gated fluorescence lifetime imaging (FLIM) system extended to perform time-resolved fluorescence anisotropy imaging (TR-FAIM). Upon excitation with linearly polarized laser pulses, the parallel and perpendicular components of the fluorescence emission from a sample are imaged simultaneously using a polarization-resolved imager. The imaging technique presented here quantitatively reports the rotational mobility of a fluorophore as it varies according to the local environment. In a single acquisition run it yields maps of both rotational correlation time and fluorescence lifetime as they vary across a sample. TR-FAIM has been applied to imaging standard multiwell plate samples of rhodamine 6G dissolved in methanol, ethylene glycol, trimethylene glycol, and glycerol. The observed rotational correlation times and fluorescence lifetimes, which report the local viscosity and refractive index of the local rhodamine 6G environment, respectively, are in good agreement with previously published single point measurements. By considering the linear dependence of the rotational correlation time on viscosity up to 20 cP, we are able to obtain a two-dimensional viscosity map. Wide-field maps of rotational correlation time, and therefore viscosity, have been obtained. This illustrates the potential to image the local viscosity and fluorescence lifetime distributions of fluorophore tagged proteins in cells.