The polarization dependence (linear dichroism) of the C 1s X-ray absorption spectrum of individual multi-walled carbon nanotubes (MWCNTs) is measured using scanning transmission X-ray microscopy. A very strong dichroic effect is found in the C 1s → π* transition, with almost complete disappearance of this transition when the electric-field (E)-vector is aligned parallel to high-quality (low-defect) MWCNTs and maximum intensity when the E-vector is orthogonal to the tube axis. In contrast, there is very little dichroism in the C 1s → σ* transitions. The origin of this polarization effect is explained. The magnitude of the polarization dependence is found to differ in MWCNTs synthesized by different methods (arc discharge versus chemical vapor deposition). This is ascribed to differences in densities of sp²-type defects. The potential for use of this signal to characterize defects in single-carbon-nanotube devices is discussed.