We consider the inclusion of TeV-scale, fermionic dark matter in an asymptotically safe model of a gauged baryon number that has been recently proposed [Phys. Rev. D 106, 035015 (2022)] The new gauge boson serves as a portal between the dark and the visible sectors. The range of the baryon number gauge coupling and the kinetic mixing between baryon number and hypercharge are constrained by the requirement that nontrivial ultraviolet fixed points are reached. We show that this asymptotically safe dark matter model can achieve the correct dark matter relic density while remaining consistent with direct detection bounds.