The controlled actuation of hydraulic and pneumatic actuators has unveiled fresh and thrilling opportunities for designing mobile robots with adaptable structures. Previously reported rolling robots, which were powered by fluidic systems, often relied on complex principles, cumbersome pump and valve systems, and intricate control strategies, limiting their applicability in other fields. In this investigation, we employed a distinct category of functional fluid identified as Electrohydrodynamic (EHD) fluid, serving as the pivotal element within the ring-shaped actuator. A short stream of functional fluid is placed within a fluidic channel and is then actuated by applying a direct current voltage aiming at shifting the center of mass of the robot and finally pushed the actuator to roll. We designed a ring-shaped fluidic robot, manufactured it using digital machining methods, and evaluated the robot's characteristics. Furthermore, we developed static and dynamic models to analyze the oscillation and rolling motion of the ring-shaped robots using the Lagrange method. This study is anticipated to contribute to the expansion of current research on EHD flexible actuators, enabling the realization of complex robotic systems.