Fluorescence anisotropy measurements reveal a non-monotonic density dependence for average rotation time (tau(R)) of a polar solute, coumarin 153 (C153) in polar supercritical fluoroform (CHF3). The conventional Stokes-Einstein-Debye model, relating tau(R) to the solvent viscosity, fails to explain the observed density dependence, because the experimental viscosity increases monotonously with density for a fluid, in general. Here, the density-dependent tau(R) is calculated by incorporating the wave vector-dependent viscosity of the solvent and the solute-solvent interaction. A molecular hydrodynamic description is used for the wave vector-dependent viscosity which is verified by molecular dynamics (MD) simulation. A justification for the applicability of the present prescription is provided by reproducing the experimental viscosity of supercritical (SC) CHF3. Solute solvent interaction has been included via the fluctuating torque acting on the rotating solute. Incorporation of wave vector-dependent viscosity leads to a qualitative description of the experimental density dependence of tau(R) which is further improved upon inclusion of solute-solvent interaction.