Robotic grippers serve as the interface between a robot and the manipulated object and play a key role in accurate and safe object handling. When a gripper lacks the capability to reorient the grasped object, the range of feasible operations is limited, particularly in robots with a restricted number of DOF, such as Delta parallel robots. In this study, a parallel two-finger robotic gripper with three rotational DOFs and grasping-force control was designed and fabricated for modular integration with a Delta parallel robot. The gripper was designed to minimize weight and dimensions while maintaining the robot’s agility and workspace. A parallel arrangement of servo motors and a combination of metallic and plastic components were employed to achieve a compact structure. A tactile sensor was integrated to measure the contact force and enable control of the grasping force. The developed gripper provides rotational ranges of 360° about the vertical axis, 90° about the horizontal axis, and 180° about the axis perpendicular to the horizontal axis. The angular command increment is 1°. The grasping force is adjustable from 0.5 to 5 N in increments of 0.1 N. Experimental tests were conducted to evaluate the rotational motion about the three axes and the grasping-force control capability. The results demonstrated stable operation in both rotational motion and grasping-force control, indicating that the proposed gripper can effectively extend the operational capabilities of Delta parallel robots through modular integration.