In this work, we investigate the constraints on anapole dark matter characterized by its derivative coupling to standard model photons. This momentum-dependent interaction significantly enhances the scattering between dark matter and standard model states within compact stars making celestial capture a valuable probe of such tiny interactions. We find that for higher dark matter masses, constraints derived from solar neutrinos produced by captured dark matter are more stringent than those obtained by the recent DarkSide-50 and LUX-ZEPLIN experiments. Additionally, we demonstrate that the projected sensitivity from observing cold neutron stars in the near future offers the potential to explore much deeper regions of the parameter space.