The Hanle effect is a relatively new magnetic diagnostic in stellar astrophysics. Although a substantial literature exists for applications of the Hanle effect in solar studies, the Hanle effect is only a fledgling subject in stellar astrophysics, with previous work focusing on simplistic cases to isolate the magnetic effects on polarized resonance scattering line profiles. In particular, applications to stars have treated the star as a point source of illumination. This paper carries the work forward by considering the consequences of finite stellar size for the line polarization. An approach based on intensity moments is derived. For optically thin line scattering and a star that is uniformly bright, the effect of finite star illumination is shown to produce the familiar finite star depolarization factor found by Cassinelli, Nordsieck, & Murison in 1987 for Thomson scattering by free electrons. An illustrative case is examined to show how the depolarization factor and magnetic field distribution affect the spatial sensitivity of the Hanle effect as a magnetic diagnostic