Fluid-driven robotic systems typically use bulky and rigid power supplies, considerably limiting their mobility and flexibility. Although various forms of low-profile soft pumps have been demonstrated, they either are limited to specific working fluids or generate limited flow rates or pressures, making them ill-suited for widespread robotics applications. In this work, we introduce a class of centimeter-scale soft peristaltic pumps for power and control of fluidic robots. An array of high power density robust dielectric elastomer actuators (DEAs) (each weighing 1.7 grams) were adopted as soft motors, operated in a programmed pattern to produce pressure waves in a fluidic channel. We investigated and optimized the dynamic performance of the pump by analyzing the interaction between the DEAs and the fluidic channel with a fluid-structure interaction finite element model. Our soft pump achieved a maximum blocked pressure of 12.5 kilopascals and a run-out flow rate of 39 milliliters per minute with a response time of less than 0.1 second. The pump can generate bidirectional flow and adjustable pressure through control of drive parameters such as voltage and phase shift. Furthermore, the use of peristalsis makes the pump compatible with various liquids. To illustrate the versatility of the pump, we demonstrate mixing a cocktail, powering custom actuators for haptic devices, and performing closed-loop control of a soft fluidic actuator. This compact soft peristaltic pump opens up possibilities for future on-board power sources for fluid-driven robots in a variety of applications, including food handling, manufacturing, and biomedical therapeutics.