  We consider the nondynamical Chern-Simons (CS) modification to General
Relativity (GR) in the framework of the Einstein-Cartan formulation, as
providing a way to incorporate a slowly rotating Kerr black hole in the space
of solutions. Our proposal lies on considering the CS term as a source of
torsion and on an iterative procedure to look for vacuum solutions of the
system, by expanding the tetrad, the connection and the embedding parameter, in
powers of a dimensionless small parameter $\beta$ which codifies the CS
coupling. Starting from a torsionless zeroth-order vacuum solution we derive
the second-order differential equation for the $\mathcal{O}(\beta)$ corrections
to the metric, for an arbitrary embedding parameter. Furthermore we can show
that the slowly rotating Kerr metric is an $\mathcal{O}(\beta)$ solution of the
system either in the canonical or the axial embeddings.
