We demonstrate that the observation of old strange quark stars (SQSs) can set important limits on the scattering cross-sections between light quarks and non-interacting scalar dark matter (DM). By analyzing a set of 1403 solitary pulsar-like compact stars in the Milky Way, we find that the old solitary pulsar PSR J1801-0857D can set the most stringent upper limits on or the cross-sections between DM and protons. By converting into based on effective operator analyses, we show that the resulting limit, by assuming PSR J1801-0857D is an SQS, is comparable with that of the current direct detection experiments in terrestrial labs but weaker by several orders of magnitude than that obtained by assuming PSR J1801-0857D is a neutron star (NS), which requires an extremely small far beyond the limits of direct detection experiments. Our findings imply that old pulsars are more likely to be identified as SQSs than as NSs in future terrestrial experiments observing scalar DM.
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