  Aims. We aim to expand our understanding of radio wave emission and
propagation in the pulsar magnetosphere by studying the polarization of
drifting sub-pulses in highly sensitive observations of PSR~B1919+21 recorded
at the Arecibo Observatory.
  Methods. We apply and compare several methods of analysis and visualization,
including eigenvalue analysis of the longitude-resolved covariances between the
Stokes parameters; longitude-resolved scatter plots of the normalised Stokes
vectors in the Poincar\'e sphere; auto- and cross-correlations between the
Stokes parameters as a function of offset in pulse longitude and lag in pulse
number; and mean drift bands of polarization state, formed by averaging the
Stokes parameters and quantities derived from them synchronously with the
drifting sub-pulse modulation period.
  Results. We observe regions of pulse longitude where the superposition of
orthogonally polarised modes is best described as incoherent and regions where
the superposition appears to be at least partially coherent. Within the region
of coherent superposition, over a range of pulse longitudes spanning $\sim
2\circ$, the distribution of the Stokes polarization vectors forms a torus
centered near the origin of the Poincar\'e sphere. Furthermore, the
polarization vectors rotate about the axis of revolution of the torus
synchronously with the drifting sub-pulse modulation of the total intensity.
  Conclusions. The nearly uniform circular modulation of polarization state,
clearly evident in both the toroidal distribution of the Stokes polarization
vectors and the mean drift bands of the Stokes parameters, is not predicted by
current theoretical models of pulsar emission. We propose different scenarios
to explain the generation of the torus, based on either incoherent or
phase-coherent superposition of orthogonally polarised modes.
