Soft-gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are slowly rotating, isolated neutron stars that sporadically undergo episodes of long-term flux enhancement (outbursts) generally accompanied by the emission of short bursts of hard X-rays(1,2). This behaviour can be understood in the magnetar model(3-5), according to which these sources are mainly powered by their own magnetic energy. This is supported by the fact that the magnetic fields inferred from several observed properties(6-8) of SGRs and AXPs are greater than-or at the high end of the range of-those of radio pulsars. In the peculiar case of SGR 0418+5729, a weak dipole magnetic moment is derived from its timing parameters(9), whereas a strong field has been proposed to reside in the stellar interior(10,11) and in multipole components on the surface(12). Here we show that the X-ray spectrum of SGR 0418+5729 has an absorption line, the properties of which depend strongly on the star's rotational phase. This line is interpreted as a proton cyclotron feature and its energy implies a magnetic field ranging from 2x10(14) gauss to more than 10(15) gauss.