Stars orbiting Sgr A* at the Milky Way’s center provide a unique laboratory to test gravity and dark matter (DM). We demonstrate that DM interactions in stellar interiors induce a novel momentum transfer force, altering orbits beyond gravitational effects. We derive the first astrophysical constraints on DM-nucleon scattering using S2’s 2000-2019 orbital data probing sub-GeV parameter space for specified DM distributions near Sgr A*. We further show that complementary orbital survival constraints and future observations of highly eccentric S-stars extend the reach to DM profiles allowed by present gravitational measurements. Unlike bounds requiring DM capture and annihilation, our constraints apply broadly to scattering DM including asymmetric DM, and extend to masses where methods based on capture can lose sensitivity. Stellar lifetime constraints over Myr timescales complement these, surpassing some direct detection and cosmological limits. This work establishes stellar dynamics as a novel probe of DM interactions.