We report the first measurement of the double-differential and total muon neutrino charged current inclusive cross sections on argon at a mean neutrino energy of 0.8 GeV. Data were collected using the MicroBooNE liquid argon time projection chamber located in the Fermilab Booster neutrino beam and correspond to 1.6×10^{20} protons on target of exposure. The measured differential cross sections are presented as a function of muon momentum, using multiple Coulomb scattering as a momentum measurement technique, and the muon angle with respect to the beam direction. We compare the measured cross sections to multiple neutrino event generators and find better agreement with those containing more complete treatment of quasielastic scattering processes at low Q^{2}. The total flux integrated cross section is measured to be 0.693±0.010(stat)±0.165(syst)×10^{-38}  cm^{2}.