We explore the feasibility of the measurement of charm-jet cross sections in charged-current deep-inelastic scattering at the future Electron-Ion Collider. This channel provides clean sensitivity to the strangeness content of the nucleon in the high-$x$ region. We estimate charm-jet tagging performance with parametrized detector simulations. We show the expected sensitivity to various scenarios for strange parton distribution functions. We argue that this measurement will be key to future QCD global analyses, so it should inform EIC detector designs and luminosity requirements.