Numerical solutions are presented for fluid flow past a rotating elliptic cylinder placed in a uniform flow for different non-dimensional rotation rates (α). The two dimensional, incompressible Navier-Stokes equations are solved using immersed boundary method (IBM) on a non-body conforming Cartesian grid. Reynolds number based on the perimeter of elliptic cylinder is 100 and axis ratio of the cylinder is 0.1. The periodic flow, after the cylinder is impulsively started, is studied. Vortex shedding is observed in all the cases with significant differences in shedding pattern. For α ≥ 1, we observe an interesting phenomenon of formation of 'Hovering vortex’. The factors contributing to hovering vortex and associated changes in the aerodynamic forces are studied. Significant increase in lift coefficient is observed with increase in rotation rate. For some cases we observe thrust generation for major portion of the cycle. © 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.