  Light scattered off particles can become linearly polarized. Stars surrounded
by oblique, co-rotating envelopes are therefore expected to manifest periodic
linear polarimetric variations. The electron scattering magnetospheres of
magnetic massive stars are expected to be suitable candidates to observe this
effect. In this paper, we present the first semi-analytical model capable of
synthesizing the continuum polarimetric signatures of magnetic O-type stars in
an optically thin, single electron scattering limit. The purpose of this
investigation is to improve our general understanding of magnetic hot stars by
characterizing their polarimetric behaviour. Our linear polarization model is
constructed by combining the analytical expressions for the polarimetric
variations of an obliquely rotating envelope with the Analytic Dynamical
Magnetosphere model to represent a physical model for the envelope density
structure. We compute grids of model Stokes $Q$ and $U$ curves and show that
their shapes are unique to the choice of inclination and obliquity angles. We
apply our model to HD 191612, a prototypical Of?p-type star, having both
polarimetric and photometric observations. We find that the polarimetric
modulations are best reproduced with $i=19^{+12}_{-3}$$^\circ$,
$\beta=71^{+3}_{-9}$$^\circ$, and $\log \dot{M}_{B=0}=-6.11^{+0.12}_{-0.06}$
[M$_{\odot}$ yr$^{-1}$]. These results agree with previous investigations of
this star. By combining both polarimetric and photometric synthesis tools, we
simultaneously model the observations thus adding further refinement of the
wind and magnetic properties of HD 191612.
