  We measured the Rossiter-McLaughlin effect of WASP-107b during a single
transit with Keck/HIRES. We found the sky-projected inclination of WASP-107b's
orbit, relative to its host star's rotation axis, to be $|\lambda| =
{118}^{+38}_{-19}$ degrees. This confirms the misaligned/polar orbit that was
previously suggested from spot-crossing events and adds WASP-107b to the
growing population of hot Neptunes in polar orbits around cool stars. WASP-107b
is also the fourth such planet to have a known distant planetary companion. We
examined several dynamical pathways by which this companion could have induced
such an obliquity in WASP-107b. We find that nodal precession and disk
dispersal-driven tilting can both explain the current orbital geometry while
Kozai-Lidov cycles are suppressed by general relativity. While each hypothesis
requires a mutual inclination between the two planets, nodal precession
requires a much larger angle which for WASP-107 is on the threshold of
detectability with future Gaia astrometric data. As nodal precession has no
stellar type dependence, but disk dispersal-driven tilting does, distinguishing
between these two models is best done on the population level. Finding and
characterizing more extrasolar systems like WASP-107 will additionally help
distinguish whether the distribution of hot-Neptune obliquities is a dichotomy
of aligned and polar orbits or if we are uniformly sampling obliquities during
nodal precession cycles.
