  In a previous paper, we showed that the asymmetric ejecta produced by (zero
impact parameter) head-on collisions of carbon-oxygen white dwarfs allow these
progenitor models for Type Ia supernovae (SNe Ia) to cover the observed
two-dimensional (2D) distribution of Si II line depths (Branch plot). In this
paper, we study the polarization signature associated with the 2D asymmetric
ejecta of the collision model and a double-detonation model using similar
TARDIS radiative transfer simulations along different lines of sight with a
spherical photosphere, combined with a new 3D Monte Carlo polarization code. We
show that the polarization $Q$ can be parametrized as a product
$Q=Q_{\max}Q_{\rm{x}}$ of a radial structure component $Q_{\max}$ which is
insensitive to the model specifics and is shown to be universally around
$Q_{\max}\sim 5\%$, and a cancellation component $Q_{\rm{x}}$ which depends on
the asymmetry details. The continuum polarization is found to be low for both
the collision and double-detonation models with $Q\sim 0.5\%$. However, the
irregular Si distribution in the 2D head-on collision model results in Si II
line polarization reaching $Q\sim 3\%$ ($Q_{\rm{x}} \lesssim 50\%$) in tension
with observations (mostly $\lesssim 1.2\%$). In contrast, we show that the
double-detonation model also covers the Branch plot, and yet results in low
line polarization $Q\lesssim 0.7\%$ ($Q_{\rm{x}} \sim 10\%$) consistent with
previous results and most SNe Ia. These results strengthen the case for
asymmetric explosions as progenitors of SNe Ia, emphasizing an additional
requirement for large polarization cancellations to account for the low
observed line polarizations.
