Microfluidic devices and micro-pumps are increasingly necessitated in many fields ranging from untethered soft robots, to pharmaceutical and biomedical technology. While realization of such devices is limited by miniaturization constraints of conventional actuators, these restrictions can be resolved by using smart material transducers instead. This paper proposes and investigates the first ionic polymer metal composite (IPMC) actuator-driven linear peristaltic pump. With the aim of designing a monolithic device, our concept is based on a single IPMC actuator that is etched on both sides and cut with kirigami-inspired slits by laser ablation. Our pump has a planar configuration, operates with low activation voltages (< 5 V) and is simple to manufacture and thus miniaturize. We build proof-of-principle prototypes of an open and closed design of our proposed pump concept, model the closed design, and evaluate both configurations experimentally. Results show the feasibility of the proposed IPMC-driven pump. Without any optimization, the open pump achieved pumping rates of 669 pL/s, while the closed pump configuration attained a 4.57 Pa pressure buildup and 9.18 nL/s pumping rate. These results indicate feasibility of the concept, and future work will focus on design optimization.