  We show that it is possible to build up a consistent model describing a
superconducting cosmic string (SCS) endowed with torsion. A full string
solution is obtained by matching the internal and the external solutions. We
derive the deficit angle, the geodesics of and the gravitational force on a
test-particle moving under the action of this screwed SCS. A couple of
potentially observable astrophysical phenomena are highlighted: the dynamics of
compact objects orbiting torsioned SCS and the accretion of matter onto it.
