Analyses of Lunar Laser Ranging data show that the spin symmetry axis of the Moon is ahead of its expected Cassini state by an angle of ϕp = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid‐body tides and viscous core‐mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the center of the Moon can also account for a part of the observed phase lead angle ϕp. We build a rotational dynamic model of the Cassini state of the Moon that comprises an inner core, a fluid core, and a mantle and where solid regions are allowed to deform viscoelastically in response to an applied forcing. We show that the presence of an inner core does not change the global monthly Q of the Moon and, hence, that the contribution from solid‐body tides to ϕp is largely unaffected by an inner core. However, we also show that viscoelastic deformation within the inner core, acting to realign its figure axis with that of the mantle, can contribute significantly to ϕp through inner core‐mantle gravitational coupling. We show that the contribution to ϕp is largest when the inner core viscosity is in the range of 1013 to 1014 Pa s, when the inner core radius is large and when the free inner core nutation frequency approaches a resonance with the precession frequency of 2π/18.6 yr−1.

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