  In this paper we obtain the space-time generated by a time-like
current-carrying superconducting screwed cosmic string(TCSCS). This
gravitational field is obtained in a modified scalar-tensor theory in the sense
that torsion is taken into account. We show that this solution is comptible
with a torsion field generated by the scalar field $\phi $. The analysis of
gravitational effects of a TCSCS shows up that the torsion effects that appear
in the physical frame of Jordan-Fierz can be described in a geometric form
given by contorsion term plus a symmetric part which contains the scalar
gradient. As an important application of this solution, we consider the linear
perturbation method developed by Zel'dovich, investigate the accretion of cold
dark matter due to the formation of wakes when a TCSCS moves with speed $v$ and
discuss the role played by torsion. Our results are compared with those
obtained for cosmic strings in the framework of scalar-tensor theories without
taking torsion into account.
