  In diffuse molecular clouds, possible precursors of star-forming clouds, the
effect of the magnetic field is unclear. In this work we compare the
orientations of filamentary structures in the Polaris Flare, as seen through
dust emission by Herschel, to the plane-of-the-sky magnetic field orientation
($\rm B_{pos}$) as revealed by stellar optical polarimetry with RoboPol. Dust
structures in this translucent cloud show a strong preference for alignment
with $\rm B_{pos}$. 70 % of field orientations are consistent with those of the
filaments (within 30$^\circ$). We explore the spatial variation of the relative
orientations and find it to be uncorrelated with the dust emission intensity
and correlated to the dispersion of polarization angles. Concentrating in the
area around the highest column density filament, and in the region with the
most uniform field, we infer the $\rm B_{pos}$ strength to be 24 $-$ 120
$\mu$G. Assuming that the magnetic field can be decomposed into a turbulent and
an ordered component, we find a turbulent-to-ordered ratio of 0.2 $-$ 0.8,
implying that the magnetic field is dynamically important, at least in these
two areas. We discuss implications on the 3D field properties, as well as on
the distance estimate of the cloud.
