  The ARIANNA detector is designed to detect neutrinos with energies above
$10^{17}$eV. Due to the similarities in generated radio signals, cosmic rays
are often used as test beams for neutrino detectors. Some ARIANNA detector
stations are equipped with antennas capable of detecting air showers. Since the
radio emission properties of air showers are well understood, and the
polarization of the radio signal can be predicted from the arrival direction,
cosmic rays can be used as a proxy to assess the reconstruction capabilities of
the ARIANNA neutrino detector. We report on dedicated efforts of reconstructing
the polarization of cosmic-ray radio pulses. After correcting for difference in
hardware, the two stations used in this study showed similar performance in
terms of event rate and agreed with simulation. Subselecting high quality
cosmic rays, the polarizations of these cosmic rays were reconstructed with a
resolution of $2.5^{\circ}$ (68% containment), which agrees with the expected
value obtained from simulation. A large fraction of this resolution originates
from uncertainties in the predicted polarization because of the contribution of
the subdominant Askaryan effect in addition to the dominant geomagnetic
emission. Subselecting events with a zenith angle greater than $70^{\circ}$
removes most influence of the Askaryan emission, and, with limited statistics,
we found the polarization uncertainty is reduced to $1.3^{\circ}$ (68%
containment).
