[en] We present the discovery of a strongly phase-variable absorption feature in the X-ray spectrum of the nearby, thermally emitting, isolated neutron star RX J0720.4–3125. The absorption line was detected performing detailed phase-resolved spectroscopy in 20 XMM-Newton observations, covering the period 2000 May–2012 September. The feature has an energy of ∼750 eV, an equivalent width of ∼30 eV, and it is significantly detected for only ∼20% of the pulsar rotation. The absorption feature appears to be stable over the timespan covered by the observations. Given its strong dependence on the pulsar rotational phase and its narrow width, a plausible interpretation is in terms of resonant proton cyclotron absorption/scattering in a confined magnetic structure very close to the neutron star surface. The inferred field in such a magnetic loop is $B_{\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{p}}\sim <!--\; ???\; -->2\times <!--\; ??\; -->{10}^{14}$ G, a factor of ∼7 higher than the surface dipolar magnetic field.