  The Ly-alpha line of He II at 304 \AA\ is one of the spectral lines of choice
for EUV channels of narrow-band imagers on board space telescopes, which
provide spectacular intensity images of the outer solar atmosphere. Since the
magnetic field information is encoded in the polarization of the spectral line
radiation, it is important to investigate whether the He II line radiation from
the solar disk can be polarized, along with its magnetic sensitivity. Here we
report some theoretical predictions concerning the linear polarization signals
produced by scattering processes in this strong emission line of the solar
transition region, taking into account radiative transfer and the Hanle effect
caused by the presence of organized and random magnetic fields. We find that
the fractional polarization amplitudes are significant (${\sim}1%$), even when
considering the wavelength-integrated signals. Interestingly, the scattering
polarization of the Ly-alpha line of He II starts to be sensitive to the Hanle
effect for magnetic strengths B>100 G (i.e., for magnetic strengths of the
order of and larger than the Hanle saturation field of the hydrogen Ly-alpha
line at 1216 \AA). We therefore propose simultaneous observations of the
scattering polarization in both Ly-alpha lines to facilitate magnetic field
measurements in the upper solar chromosphere. Even the development of a
narrow-band imaging polarimeter for the He II 304 \AA\ line alone would be
already of great diagnostic value for probing the solar transition region.
