In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss-Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effects of the ECKS parameter on the weak deflection angle and shadow of the black hole. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing. Hence, we show that the weak deflection of black hole is increased with the increase of the ECKS parameter.