  Supersymmetric Twin Higgs models ameliorate the fine-tuning of the
electroweak scale originating from the heavy scalar top partners required by
the non-discovery of them at the Large Hadron Collider. If the Lightest
Supersymmetric Particle resides in the twin sector, it may play the role of
dark matter even if it is charged under twin gauge interactions. We show that
the twin stau is a viable candidate for charged dark matter, even if the twin
electromagnetic gauge symmetry is unbroken, with thermal relic abundance that
naturally matches the observed dark matter abundance. A wide parameter space
satisfies all the experimental constraints including those on dark matter
self-interactions. Twin stau dark matter can be observed in future direct
detection experiments such as LUX-ZEPLIN. The stau has a mass in the range of
300-500 GeV, and in the minimal scenario, has a decay length long enough to be
observed as a disappearing track or a long-lived particle at the Large Hadron
Collider.
