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

Spin-Orbit Alignment For 110-Day-Period KOI368.01 From Gravity Darkening