  We fit the \emph{Kepler} photometric light curve of the KOI-368 system using
an oblate, gravity-darkened stellar model in order to constrain its spin-orbit
alignment. We find that the system is relatively well-aligned with a
sky-projected spin-orbit alignment of $\lambda=10^{\circ}\pm2^{\circ}$, a
stellar obliquity of $\psi=3^{\circ}\pm7^{\circ}$, and a true spin-orbit
alignment of $\varphi=11^{\circ}\pm3^{\circ}$. Although our measurement differs
significantly from zero, the low value for $\varphi$ is consistent with
spin-orbit alignment. We also measure various transit parameters of the KOI-368
system: $R_{\star}=2.28\pm0.02 R_{\odot}$, $R_{p}=1.83\pm0.02R_{jup}$, and
$i=89.221^{\circ}\pm0.013^{\circ}$. This work shows that our gravity-darkened
model can constrain long-period, well-aligned planets and M-class stars
orbiting fast-rotators, allowing for measurement of a new subcategory of
transiting bodies.
