  We investigate theoretically the properties of a weak link between two
superconducting leads, which has the form of a non-superconducting nanowire
with a strong Rashba spin-orbit coupling caused by an electric field. In the
Coulomb blockade regime of single-electron tunneling, we find that such a weak
link acts as a "spin splitter" of the spin states of Cooper pairs tunneling
through the link, to an extent that depends on the direction of the electric
field. We show that the Josephson current is sensitive to interference between
the resulting two transmission channels, one where the spins of both members of
a Cooper pair are preserved and one where they are both flipped. As a result,
the current is a periodic function of the strength of the spin-orbit
interaction and of the bending angle of the nanowire (when mechanically bent);
an identical effect appears due to strain-induced spin-orbit coupling. In
contrast, no spin-orbit induced interference effect can influence the current
through a single weak link connecting two normal metals.
