Non-invasive, high-throughput spectroscopic techniques can identify chiral indices (n,m) of carbon nanotubes down to the single-tube level1–6. Yet, for complete characterization and to unlock full functionality, the handedness, the structural property associated with mirror symmetry breaking, also needs to be identified accurately and efficiently7–14. So far, optical methods fail in the handedness characterization of single nanotubes because of the extremely weak chiroptical signals (roughly 10−7) compared with the excitation light15,16. Here we demonstrate the complete structure identification of single nanotubes in terms of both chiral indices and handedness by Rayleigh scattering circular dichroism. Our method is based on the background-free feature of Rayleigh scattering collected at an oblique angle, which enhances the nanotube's chiroptical signal by three to four orders of magnitude compared with conventional absorption circular dichroism. We measured a total of 30 single-walled carbon nanotubes including both semiconducting and metallic nanotubes and found that their absolute chiroptical signals show a distinct structure dependence, which can be qualitatively understood through tight-binding calculations. Our strategy enables the exploration of handedness-related functionality of single nanotubes and provides a facile platform for chiral discrimination and chiral device exploration at the level of individual nanomaterials. Optical spectroscopy can identify chiral indices of individual carbon nanotubes, but has so far been unable to determine their handedness because of the weak chiroptical signal. Rayleigh scattering circular dichroism now enables the identification of both chiral indices and handedness of individual nanotubes.