  The tidal force from a supermassive black hole can rip apart a star that
passes close enough in what is known as a Tidal Disruption Event. Typically
half of the destroyed star remains bound to the black hole and falls back on
highly eccentric orbits, forming an accretion flow which powers a luminous
flare. In this paper we use analytical and numerical calculations to explore
the effect of stellar rotation on the fallback rate of material. We find that
slowly spinning stars ($\Omega_* \lesssim 0.01 \Omega_{\rm{breakup}}$) provide
only a small perturbation to fallback rates found in the non-spinning case.
However when the star spins faster, there can be significant effects. If the
star is spinning retrograde with respect to its orbit the tidal force from the
black hole has to spin down the star first before disrupting it, causing
delayed and sometimes only partial disruption events. However, if the star is
spinning prograde this works with the tidal force and the material falls back
sooner and with a higher peak rate. We examine the power-law index of the
fallback curves, finding that in all cases the fallback rate overshoots the
canonical $t^{-5/3}$ rate briefly after the peak, with the depth of the
overshoot dependent on the stellar spin. We also find that in general the late
time evolution is slightly flatter than the canonical $t^{-5/3}$ rate. We
therefore conclude that considering the spin of the star may be important in
modelling observed TDE lightcurves.
