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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 delta robots with soft compliant 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 modular multi-fingered hands that can execute precise and low-inertia manipulations.