Aims. We aim to expand our understanding of radio wave emission and propagation in the pulsar magnetosphere by studying the polarisation 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 visualisation, including eigenvalue analysis of the longitude-resolved covariances between the Stokes parameters; longitude-resolved scatter plots of the normalised Stokes vectors in the Poincaré 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 polarisation 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 ∼2°, the distribution of the Stokes polarisation vectors forms a torus centered near the origin of the Poincaré sphere. Furthermore, the polarisation 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 polarisation state, clearly evident in both the toroidal distribution of the Stokes polarisation 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.