Underwater swimming robots permit remote access to over 70% of the Earth's surface that is covered in water for a variety of scientific, environmental, tactical, or industrial purposes. Many practical applications for robots in this setting include sensing, monitoring, exploration, reconnaissance, or inspection tasks. In the interest of expanding this activity and opportunity within aquatic environments, this letter describes the development of a swimming robot characterized by simple, robust, and scalable design. The robot, named RoboScallop, is inspired by the locomotion of bivalve scallops, utilizing two articulating rigid shell components and a soft elastic membrane to produce water jet propulsion. A single-DoF, reciprocating crank mechanism enclosed within the shell housing of the robot is used to generate pulsating thrust, and the performance of this novel swimming method is evaluated by characterization of the robot jet force and swimming speed. This is the first time jet propulsion is demonstrated for a robot swimming in normal, Newtonian fluid using a bivalve morphology. We found the metrics of the robot to be comparable to its biological counterpart, but free from metabolic limitations which prevent sustained free swimming in living species. Leveraging this locomotion principle may provide unique benefits over other existing underwater propulsion techniques, including robustness, scalability, resistance to entanglement, and possible implicit water treatment capabilities, to drive the further development of a new class of self-contained, hybrid-stiffness underwater robots.