  Using a new geometrical method introduced by Werner, we find the deflection
angle in the weak limit approximation by a spinning cosmic string in the
context of the Einstein-Cartan (EC) theory of gravity. We begin by adopting the
String-Randers optical metric, then we apply the Gauss-Bonnet theorem to the
optical geometry and derive the leading terms of the deflection angle in the
equatorial plane. Calculations shows that light deflection is affected by the
intrinsic spin of the cosmic string and torsion.
