Soft fluidic actuators (SFAs) are widely utilized in various areas such as wearable systems due to the inherent compliance which allows safe and flexible interaction. However, SFA-driven systems generally require a large pump, multiple valves and tubes, which hinders to develop a miniaturized system with small range of motion. Thus, a highly integrated soft actuator needs to be developed for implementing a compact SFA-driven system. In this study, we propose an electro-hydraulic soft zipping actuator that can be used as a miniature pump. This actuator exerts tactile force as a dielectric liquid contained inside the actuator pressurized its deformable part. In addition, the proposed actuator can estimate the internal dielectric liquid thickness by using its self-sensing function. Besides, the electrical characteristics and driving performance of the proposed system were verified through experiments.