Detection of a surprisingly high flux of positron annihilation radiation from the inner galaxy has motivated the proposal that dark matter is made of weakly interacting light particles (possibly as light as the electron). This scenario is extremely hard to test in current high energy physics experiments. Here, however, we demonstrate that the current value of the electron anomalous magnetic moment already has the required precision to unambiguously test the light dark matter hypothesis. If confirmed, the implications for astrophysics are far-reaching.