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A Faraday rotation spectroscopy (FRS) technique is presented for measurements on the micrometer scale. Spectral acquisition speeds of about two orders of magnitude faster than state‐of‐the‐art modulation spectroscopy setups are demonstrated. The experimental method is based on charge‐coupled‐device detection, avoiding speed‐limiting components, such as polarization modulators with lock‐in amplifiers. At the same time, FRS spectra are obtained with a sensitivity of 20 µrad (0.001°\[0.001{\bm{^\circ }}\]) over a broad spectral range (525–800 nm), which is on par with state‐of‐the‐art polarization‐modulation techniques. The new measurement and analysis technique also automatically cancels unwanted Faraday rotation backgrounds. Using the setup, Faraday rotation spectroscopy of excitons is performed in a hexagonal boron nitride‐encapsulated atomically thin semiconductor WS2 under magnetic fields of up to 1.4 T at room temperature and liquid helium temperature. An exciton g‐factor of −4.4 ± 0.3 is determined at room temperature, and −4.2 ± 0.2 at liquid helium temperature. In addition, FRS and hysteresis loop measurements are performed on a 20 nm thick film of an amorphous magnetic Tb20Fe80 alloy. [ABSTRACT FROM AUTHOR]