We present 0.″075 (≈400 pc) resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of the [C ii] and dust continuum emission from the host galaxy of the z = 6.5406 quasar, P036+03. We find that the emission arises from a thin, rotating disk with an effective radius of 0.″21 (1.1 kpc). The velocity dispersion of the disk is consistent with a constant value of 66.4 ± 1.0 km s−1, yielding a scale height of 80 ± 30 pc. The [C ii] velocity field reveals a distortion that we attribute to a warp in the disk. Modeling this warped disk yields an inclination estimate of 40.°4 ± 1.°3 and a rotational velocity of 116 ± 3 km s−1. The resulting dynamical mass estimate of (1.96 ± 0.10) × 1010 M ⊙ is lower than previous estimates, which strengthens the conclusion that the host galaxy is less massive than expected based on local scaling relations between the black hole mass and the host galaxy mass. Using archival MUSE Lyα observations, we argue that counterrotating halo gas could provide the torque needed to warp the disk. We further detect a region with excess (15σ) dust continuum emission, which is located 1.3 kpc northwest of the galaxy’s center and is gravitationally unstable (Toomre Q < 0.04). We posit this is a star-forming region whose formation was triggered by the warp because the region is located within a part of the warped disk where gas can efficiently lose angular momentum. The combined ALMA and MUSE imaging provides a unique view of how gas interactions within the disk–halo interface can influence the growth of massive galaxies within the first billion years of the Universe.