  We discuss the propagation of fermions on generic, curved branes in IKKT-type
matrix models. The Dirac operator can be understood either in terms of a
Weitzenb\"ock connection, or in terms of the Levi-Civita connection with extra
torsion term. We discuss in detail the coupling of spin to the background
geometry using the JWKB approximation. Despite the absence of local Lorentz
invariance in the underlying IKKT framework, our results agree with the
expectations of Einstein-Cartan theory, and differ from general relativity only
by an extra coupling to the totally antisymmetric part of the torsion. The case
of FLRW cosmic background solutions is discussed as a special case.
