We consider a natural asymmetric dark matter (ADM) model in the mirror twin Higgs (MTH). We show that it is possible to obtain the correct dark matter (DM) abundance when a twin baryon is the DM without the need of explicit breaking of the MTH ℤ2 symmetry in the dimensionless couplings (i.e. without hard ℤ2 breaking). We illustrate how this is possible in a specific baryogenesis setup, which also leads to ADM. In the simplest scenario we obtain mDM ~ O(1) GeV, just above the proton mass. We show estimates for direct detection rates at present and future experiments.