The epoch of the formation of the first stars, known as the cosmic dawn, has emerged as a new arena in the search for dark matter. In particular, the first claimed 21-cm detection exhibits a deeper global absorption feature than expected, which could be caused by a low baryonic temperature, and has been interpreted as a sign for electromagnetic interactions between baryons and dark matter. This hypothesis has a striking prediction: large temperature anisotropies sourced by the velocity-dependent cooling of the baryons. However, in order to remain consistent with the rest of cosmological observations, only part of the dark matter is allowed to be charged and thus interactive. Here we compute, for the first time, the 21-cm fluctuations caused by a charged subcomponent of the dark matter, including both the pre- and postrecombination evolution of all fluids. We find that, for the same parameters that can explain the anomalous 21-cm absorption signal, any percent-level fraction of charged dark matter would source novel 21-cm fluctuations with a unique acoustic spectrum, and with an amplitude above any other known effects. These fluctuations are uncorrelated with the usual adiabatic anisotropies, and would be observable at high significance with interferometers such as the Low-Frequency Array and the Hydrogen Epoch of Reionization Array, thus providing a novel probe of dark matter at cosmic dawn.