Traditional parallel-jaw grippers are insufficient for delicate object manipulation due to their stiffness and lack of dexterity. Other dexterous robotic hands often have bulky fingers, rely on complex time-varying cable drives, or are prohibitively expensive. In this paper, we introduce a novel low-cost compliant gripper with two centimeter-scaled 3-DOF delta robots using off-the-shelf linear actuators and 3D-printed soft materials. To model the kinematics of soft compliant delta links which diverge from typical rigid links, we train neural networks using a perception system. Furthermore, we analyze the delta robot's force profile by varying the starting position in its workspace and measuring the resulting force from a push action. Finally, we demonstrate the compliance and dexterity of our gripper through six dexterous manipulation tasks involving small and delicate objects. Thus, we present the groundwork for creating multi-fingered hands that can execute precise and low-inertia manipulations.