The characterization of scattered light is complex and relatively nonstandardized despite being of great importance to many optical technologies. While total scatter can be efficiently measured using integrating-sphere-based techniques, a detailed determination of the full bidirectional scattering distribution function is far more challenging, often requiring complicated and expensive equipment as well as substantial measurement time. Due to this, many research groups rely on simpler, angle-resolved scattering (ARS) measurements, yet these are typically carried out using a single wavelength source, therefore providing limited information. Here, we demonstrate a custom-built broadband angle-resolved optical spectrometer, which utilizes a supercontinuum white light laser source combined with a custom automated goniometer and a Si CCD array spectrometer in order to carry out broad spectral measurements of ARS. The use of a collimated supercontinuum allows for small area measurements that are often crucial for investigation of nanophotonic samples created using expensive fabrication techniques. The system has been tested and calibrated, and accuracy and reproducibility have been verified by integrating wavelength and ARS data over the angular range and comparing to calibrated integrating sphere measurements.