The alternating current (AC) conductivity in semiconductor crystals with an open-core screw dislocation is studied in the current work. The screw dislocation in crystalline media results in an effective potential field which affects the electronic transport properties of the system. Therefore, from a technological view point, it is interesting to investigate properties of AC conductivity at frequencies of a few terahertz. To quantify the screw-induced potential effect, we calculated the AC conductivity of dislocated crystals using the Kubo formula. The conductivity showed peaks within the terahertz frequency region, where the amplitude of the AC conductivity was large enough to be measured in experiments. The measurable conductivity peaks did not arise in dislocation-free crystals threaded by a magnetic flux tube. These results imply different conductivity mechanisms in crystals with a screw dislocation than those threaded by a magnetic flux tube, despite the apparent similarity in their electronic eigenstates.