Two-dimensional incompressible, viscous fluid flow around a rotationally oscillating circular cylinder is studied numerically by using a recently developed higher order compact finite difference scheme (HOC) at Reynolds number Re = 500. The stream function vorticity formulation of Navier Stokes equations in cylindrical polar coordinates are considered as the governing equations. Different values of peak rotation rate $\alpha$m and forced oscillation frequency fe are considered. The simulated results are in a good agreement both qualitatively and quantitatively with the previously published results. {\textcopyright} (2013) Trans Tech Publications, Switzerland.