A combined experimental and theoretical study is carried out to probe the rotational behavior of red blood cells (RBCs) in a single beam optical trap. We induce shape changes in RBCs by altering the properties of the suspension medium in which live cells float. We find that certain shape anisotropies result in the rotation of optically trapped cells. Indeed, even normal (healthy) RBCs can be made to rotate using linearly polarized trapping light by altering the osmotic stress the cells are subjected to. Hyperosmotic stress is found to induce shape anisotropies. We also probe the effect of the medium's viscosity on cell rotation. The observed rotations are modeled using a Langevin-type equation of motion that takes into account frictional forces that are generated as RBCs rotate in the medium. We observe good correlation between our measured data and calculated results.