  We consider the Mielke-Baekler model of three-dimensional AdS gravity with
torsion, which has gravitational and translational Chern-Simons terms in
addition to the usual Einstein-Hilbert action with cosmological constant. It is
shown that the topological nature of the model leads to a finite
Fefferman-Graham expansion. We derive the holographic stress tensor and the
associated Ward identities and show that, due to the asymmetry of the left- and
right-moving central charges, a Lorentz anomaly appears in the dual conformal
field theory. Both the consistent and the covariant Weyl and Lorentz anomaly
are determined, and the Wess-Zumino consistency conditions for the former are
verified. Moreover we consider the most general solution with flat boundary
geometry, which describes left-and right-moving gravitational waves on AdS_3
with torsion, and shew that in this case the holographic energy-momentum tensor
is given by the wave profiles. The anomalous transformation laws of the wave
profiles under diffeomorphisms preserving the asymptotic form of the bulk
solution yield the central charges of the dual CFT and confirm the results that
appeared earlier on in the literature. We finally comment on some points
concerning the microstate counting for the Riemann-Cartan black hole.
