  A toric arrangement is a finite set of hypersurfaces in a complex torus,
every hypersurface being the kernel of a character. In the present paper we
build a CW-complex homotopy equivalent to the arrangement complement, with a
combinatorial description similar to that of the well-known Salvetti complex.
If the toric arrangement is defined by a Weyl group we also provide an
algebraic description, very handy for cohomology computations. In the last part
we give a description in terms of tableaux for a toric arrangement appearing in
robotics.
