A Faraday rotation experiment can set limits on the magnetic moment of a electrically-neutral, dark-matter particle, and the limits increase in stringency as the candidate-particle mass decreases. Consequently, if we assume the dark-matter particle to be a thermal relic, our most stringent constraints emerge at the keV mass scale. We discuss how such an experiment could be realized and determine the limits on the magnetic moment as a function of mass which follow given demonstrated experimental capacities.