We report on a novel micro-spectroscopic technique to quantitatively measure the extinction cross-section σ(ext) of few and single linearly polarizing nano-antennas. This technique relies on rotating the linear polarization of a monochromatic laser beam at a frequency ω(1) while optically chopping the incident beam at ω(2) and using lock-in detection with a switched reference frequency input to measure the amount of scattered and absorbed power. The amount of power removed from the beam corresponds to σ(ext) of the polarizing nano-structure. Furthermore, this technique is easy to integrate into existing microscopy or micro-photoluminescence setups and does not depend on the sample's temperature.