We report the first measurement of the neutron cross section on argon in the energy range of 100-800 MeV. The measurement was obtained with a 4.3-hour exposure of the Mini-CAPTAIN detector to the WNR/LANSCE beam at LANL. The total cross section is measured from the attenuation coefficient of the neutron flux as it traverses the liquid argon volume. A set of 2,631 candidate interactions is divided in bins of the neutron kinetic energy calculated from time-of-flight measurements. These interactions are reconstructed with custom-made algorithms specifically designed for the data in a time projection chamber the size of the Mini-CAPTAIN detector. The energy averaged cross section is $0.91 pm{} 0.10~mathrm{(stat.)} pm{} 0.09~mathrm{(sys.)}~mathrm{barns}$. A comparison of the measured cross section is made to the GEANT4 and FLUKA event generator packages.