  The radio polarization characteristics of millisecond pulsars (MSPs) differ
significantly from those of non-recycled pulsars. In particular, the position
angle (PA) swings of many MSPs deviate from the S-shape predicted by the
rotating vector model, even after relativistic aberration is accounted for,
indicating that they have non-dipolar magnetic geometries, likely due to a
history of accretion. Stokes tomography uses phase portraits of the Stokes
parameters as a diagnostic tool to infer a pulsar's magnetic geometry and
orientation. This paper applies Stokes tomography to MSPs, generalizing the
technique to handle interpulse emission. We present an atlas of look-up tables
for the Stokes phase portraits and PA swings of MSPs with current-modified
dipole fields, filled core and hollow cone beams, and two empirical linear
polarization models. We compare our look-up tables to data from 15 MSPs and
find that the Stokes phase portraits for a current-modified dipole
approximately match several MSPs whose PA swings are flat or irregular and
cannot be reconciled with the standard axisymmetric rotating vector model. PSR
J1939+2134 and PSR J0437$-$4715 are modelled in detail. The data from PSR
J1939+2134 at 0.61\,GHz can be fitted well with a current-modified dipole at
$(\alpha, i) = (22 \pm 2^\circ, 80 \pm 1^\circ)$ and emission altitude 0.4
$r_\text{LC}$. The fit is less accurate for PSR J1939+2134 at 1.414\,GHz, and
for PSR J0437$-$4715 at 1.44\,GHz, indicating that these objects may have a
more complicated magnetic field geometry, such as a localized surface anomaly
or a polar magnetic mountain.
