  We show that the interplay between antiferromagnetic interaction and hole
motion gives rise to a topological superconducting phase. This is captured by
the one dimensional anisotropic $t-J$ model which can be experimentally
achieved with ultracold polar molecules trapped onto an optical lattice. As a
function of the anisotropy strength we find that different quantum phases
appear, ranging from a gapless Luttinger liquid to spin gapped conducting and
superconducting regimes. In presence of appropriate $z$-anisotropy, we also
prove that a phase characterized by non-trivial topological order takes place.
The latter is described uniquely by a finite non local string parameter and
presents robust edge spin fractionalization. These results allow to explore
quantum phases of matter where topological superconductivity is induced by the
interaction.
