We report the first electron neutrino cross section measurements on argon, based on data collected by the ArgoNeuT experiment running in the GeV-scale NuMI beamline at Fermilab. A flux-averaged νe + νe total and a lepton angle differential cross section are extracted using 13 νe and νe events identified with fully automated selection and reconstruction. We employ electromagnetic-induced shower characterization and analysis tools developed to identify νe / νe-like events among complex interaction topologies present in ArgoNeuT data ( ⟨ E νe ⟩ = 4.3     GeV and ⟨ E νe ⟩ = 10.5     GeV ). The techniques are widely applicable to searches for electron-flavor appearance at short and long baseline using liquid argon time projection chamber technology. Notably, the data-driven studies of GeV-scale νe / νe interactions presented here probe an energy regime relevant for future DUNE oscillation physics.