There has been a long-standing interest in Raman spectroscopic investigation of optically trapped single functional cells. Optical trapping using a Gaussian beam has helped researchers for decades to investigate single cells suspended in a physiological medium. However, complete and sensitive probing of single cells demands further advancements in experimental methods. Herein, we propose optical trapping and simultaneous micro-Raman spectroscopy of red blood cells (RBCs) in an unconventional face-on orientation using an optical vortex beam. Using this novel method, we are successful in comparing the conformational state of hemoglobin (Hb) molecules near the RBC membrane and inside the bulk of the cell. This method enabled us to successfully probe the oxy/deoxy ratio of Hb molecules near the RBC membrane and inside the bulk of the cell. Because of the face-on orientation, the Raman spectra of RBCs acquired using a vortex beam have a significant contribution from membrane components compared to that recorded using the Gaussian beam.