Scattering of high energy particles from nucleons probes their structure, as was done in the experiments that established the non-zero size of the proton using electron beams1. The use of charged leptons as scattering probes enables measuring the distribution of electric charges, which is encoded in the vector form factors of the nucleon2. Scattering weakly interacting neutrinos gives the opportunity to measure both vector and axial vector form factors of the nucleon, providing an additional, complementary probe of their structure. The nucleon transition axial form factor, FA, can be measured from neutrino scattering from free nucleons, νμn → μ−p and ν¯ μp→ μ+n, as a function of the negative four-momentum transfer squared (Q2). Up to now, FA(Q2) has been extracted from the bound nucleons in neutrino–deuterium scattering3–9, which requires uncertain nuclear corrections10. Here we report the first high-statistics measurement, to our knowledge, of the ν¯μp→μ+n cross-section from the hydrogen atom, using the plastic scintillator target of the MINERvA11 experiment, extracting FA from free proton targets and measuring the nucleon axial charge radius, rA, to be 0.73 ± 0.17 fm. The antineutrino–hydrogen scattering presented here can access the axial form factor without the need for nuclear theory corrections, and enables direct comparisons with the increasingly precise lattice quantum chromodynamics computations12–15. Finally, the tools developed for this analysis and the result presented are substantial advancements in our capabilities to understand the nucleon structure in the weak sector, and also help the current and future neutrino oscillation experiments16–20 to better constrain neutrino interaction models.