  We present simultaneous high-precision optical polarimetric and near-infrared
(NIR) to ultraviolet (UV) photometric observations of low-mass black hole X-ray
binary A0620$\unicode{x2013}$00 in the quiescent state. Subtracting
interstellar polarization, estimated from a sample of field stars, we derive
the intrinsic polarization of A0620$\unicode{x2013}$00. We show that the
intrinsic polarization degree (PD) is variable with the orbital period with the
amplitude of $\sim0.3\%$ at least in the $R$ band, where the signal-to-noise
ratio of our observations is the best. It implies that some fraction of the
optical polarization is produced by scattering of stellar radiation off the
matter that follows the black hole in its orbital motion. In addition, we see a
rotation of the orbit-average intrinsic polarization angle (PA) with the
wavelength from $164\deg$ in the $R$ to $180\deg$ in the $B$ band. All of the
above, combined with the historical NIR to optical polarimetric observations,
shows the complex behavior of average intrinsic polarization of
A0620$\unicode{x2013}$00 with the PA making continuous rotation from infrared
to blue band by $\sim56\deg$ in total, while the PD $\sim1\%$ remains nearly
constant over the entire spectral range. The spectral dependence of the PA can
be described by Faraday rotation with the rotation measure of RM=$-0.2$ rad
$\mu$m$^{-2}$, implying a few Gauss magnetic field in the plasma surrounding
the black hole accretion disk. However, our preferred interpretation for the
peculiar wavelength dependence is the interplay between two polarized
components with different PAs. Polarimetric measurements in the UV range can
help distinguishing between these scenarios.
