  The Hanle effect has been proposed as a new diagnostic of circumstellar
magnetic fields for early-type stars, for which it is sensitive to field
strengths in the 1-300 G range. In this paper we compute the polarized P-Cygni
line profiles that result from the Hanle effect. For modeling the polarization,
we employ a variant of the ``last scattering approximation''. For cases in
which the Sobolev optical depths are greater than unity, the emergent line
intensity is assumed to be unpolarized; while for smaller optical depths, the
Stokes source functions for the Hanle effect with optically thin line
scattering are used. For a typical P Cygni line, the polarized emission forms
in the outer wind, because the Sobolev optical depth is large at the inner
wind. For low surface field strengths, weak P Cygni lines are needed to measure
the circumstellar field. For high values of the surface fields, both the Zeeman
and Hanle diagnostics can be used, with the Zeeman effect probing the
photospheric magnetic fields, and the Hanle effect measuring the magnetic field
in the wind flow. Polarized line profiles are calculated for a self-consistent
structure of the flow and the magnetic geometry based on the WCFields model,
which is applicable to slowly rotating stellar winds with magnetic fields drawn
out by the gas flow. For surface fields of a few hundred Gauss, we find that
the Hanle effect can produce line polarizations in the range of a few tenths of
a percent up to about 2 percent.
