  We study polar molecules with long-range dipole-dipole interactions confined
to move on a two-leg ladder for different orientations of the molecular dipole
moments with respect to the ladder. Matrix product states are employed to
calculate the many-body ground state of the system as function of lattice
filling fractions, perpendicular hopping between the legs, and dipole
interaction strength. We show that the system exhibits zig-zag ordering when
the dipolar interactions are predominantly repulsive. As a function of dipole
moment orientation with respect to the ladder, we find that there is a critical
angle at which ordering disappears. This angle is slightly larger than the
angle at which the dipoles are non-interacting along a single leg. This
behavior should be observable using current experimental techniques.
