The recent core technologies developed in automobile and aerospace industries can be classified into two types, namely, advancement technology for safety and convenience and mechanical technology for eco-friendly and lightweight systems. Research in the field of composite materials has attracted significant attention. Carbon-fiber-reinforced plastics (CFRP) show high specific stiffness and specific strength compared with metallic materials. They exhibit mechanical properties with high damping characteristics and are lightweight. However, according to the direction of a laminate or its stacking sequence, the structural characteristics of CFRPs vary. It is hard to predict fracture under tensile and bending forces in CRFPs, when compared to metals. Threaded fasteners with easy assembly and disassembly are used widely in several fields. However, to maintain clamping force, proper torque force should be applied. As the size of the components decreases, the clamping force also decreases because the contact area between the component and other components decreases. In this study, CFRP specimens were subjected to tensile tests via a universal testing machine to estimate their mechanical properties with respect to the stacking angles of the laminates. The reverse screw torque and screw torque at each stacking angle were determined using a torque tester after tapping holes on the CFRP specimens. It was expected that both the epoxy attached to the screw surface and stacking direction of CFRP laminates affect the screw torque force of the composite material. In the case of woven composite specimens, there was no difference observed even when torque was applied to prevent loosening of the specimens with or without coating. The average results for the woven composite specimens were better than that for the other specimens.