  Context. The Ap stars that rotate extremely slowly, with periods of decades
to centuries, represent one of the keys to the understanding of the processes
leading to the differentiation of stellar rotation.
  Aims. We characterise the variations of the magnetic field of the Ap star HD
50169 and derive constraints about its structure.
  Methods. We combine published measurements of the mean longitudinal field
<Bz> of HD 50169 with new determinations of this field moment from circular
spectropolarimetry obtained at the 6-m telescope BTA of the Special
Astrophysical Observatory of the Russian Academy of Sciences. For the mean
magnetic field modulus <B>, literature data are complemented by the analysis of
ESO spectra, both newly acquired and from the archive. Radial velocities are
also obtained from these spectra.
  Results. We present the first determination of the rotation period of HD
50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Ap
star for which magnetic field measurements have been obtained over more than a
full cycle. The variation curves of both <Bz> and <B> have a significant degree
of anharmonicity, and there is a definite phase shift between their respective
extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its
orbital elements, and suggest that the secondary is probably a dwarf star of
spectral type M.
  Conclusions. The shapes and mutual phase shifts of the derived magnetic
variation curves unquestionably indicate that the magnetic field of HD 50169 is
not symmetric about an axis passing through its centre. Overall, HD 50169
appears similar to the bulk of the long-period Ap stars.
