We report an angle resolved photoemission spectroscopy study of quantum critical scaling in the single-particle spectral function of a novel anisotropic metal Li_{0.9}Mo_{6}O_{17}. We find a temperature (T) scaling exponent value and also low-T angle resolved photoemission spectroscopy line shapes that are very challenging for current one-dimensional theory frameworks. These results add a new spectroscopic component to a growing collection of puzzling low-T transport behaviors of this material.