We report measurements of the full intrinsic optical anisotropy of isolated single-wall carbon nanotubes (SWNTs). By combining absorption spectroscopy with transmission ellipsometry and polarization-dependent resonant Raman scattering, we obtain the real and imaginary parts of the SWNT permittivity from aligned semiconducting SWNTs dispersed in stretched polymer films. Our results are in agreement with theoretical predictions, highlighting the limited polarizability of excitons in a quasi-1D system.