  This paper extends the result of \cite{BM} on the homogenization of integral
functionals with linear growth defined for Sobolev maps taking values in a
given manifold. Through a $\Gamma$-convergence analysis, we identify the
homogenized energy in the space of functions of bounded variation. It turns out
to be finite for $BV$-maps with values in the manifold. The bulk and Cantor
parts of the energy involve the tangential homogenized density introduced in
\cite{BM}, while the jump part involves an homogenized surface density given by
a geodesic type problem on the manifold.
