  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 $\nu_e + \overline{\nu}_e$ total and
a lepton angle differential cross section are extracted using 13 $\nu_e$ and
$\overline{\nu}_e$ events identified with fully-automated selection and
reconstruction. We employ electromagnetic-induced shower characterization and
analysis tools developed to identify $\nu_e/\overline{\nu}_e$-like events among
complex interaction topologies present in ArgoNeuT data ($\langle
E_{\bar{\nu}_e} \rangle = 4.3$ GeV and $\langle E_{\nu_e} \rangle = 10.5$ 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
$\nu_e/\overline{\nu}_e$ interactions presented in this Letter probe an energy
regime relevant for future DUNE oscillation physics.
