We study the tunneling of conduction electrons through a (110)-oriented single-barrier heterostructure grown from III-V semiconductor compounds. It is shown that, due to low spatial symmetry of such a barrier, the tunneling current through the barrier leads to an electron spin polarization. The inverse effect, generation of a direct tunneling current by spin polarized electrons, is also predicted. We develop the microscopic theory of the effects and show that the spin polarization emerges due to the combined action of the Dresselhaus spin-orbit coupling within the barrier and the Rashba spin-orbit coupling at the barrier interfaces.