Two-photon polarization fluorescence microscopy is used to study the nature of the emission and nonlinear absorption dipole of single CdSe/ZnS quantum rods. Rods showed strongly polarized nonlinear excitation with sharp angular dependence, following a cos(4)(phi) functional form, in agreement with the predicted two-photon absorption process. The two-photon absorption is parallel to the emission polarization and allows high orientation selectivity in excitation to be achieved. This further demonstrates the role of single molecule measurements in unraveling basic principles of light-matter interactions otherwise masked by ensemble averaging.