  Dark Matter (DM) may have a relic density that is in part determined by a
particle/antiparticle asymmetry, much like baryons. If this is the case, it can
accumulate in stars like the Sun to sizable number densities and annihilate to
Standard Model (SM) particles including neutrinos. We show that the combination
of neutrino telescope and direct detection data can be used in conjunction to
determine or constrain the DM asymmetry from data. Depending on the DM mass,
the current neutrino data from Super-K and IceCube give powerful constraints on
asymmetric DM unless its fractional asymmetry is $\lesssim 10^{-2}$. Future
neutrino telescopes and detectors like Hyper-K and KM3NeT can search for the
resulting signal of high-energy neutrinos from the center of the Sun. The
observation of such a flux yields information on both the DM-nucleus cross
section but also on the relative abundances of DM and anti-DM.
