There is a rich diversity of flagellar swimmers in nature. In general, they use a long tail, known as flagellum or celia, to propel themselves in fluids. Due to their small size, the fluid around them appears as viscous, resulting in low Reynolds number dynamics. Thus, there is no inertial component in the propulsion. Until to date, there is no engineered low Reynolds number swimmer that can propel itself autonomously. Earlier efforts resulted in swimmers that are driven by external magnetic fields. Here we present a swimmer that propels itself autonomously by using live rat cardiomyocytes. The swimmer consists of a flexible tail and a rigid head. Cardiomyocytes are plated on the tail near the head. The cells self-organize themselves by interacting with the flexible tail substrate, and with each other, and emerge as a group all beating in synchrony. The cell forces bend and deform the tail with time against the viscous drag of the fluid. This fluid-structure interaction results in a bending wave that travels from head to the tail end giving rise to a time irreversible dynamics. Such motion results in a net propulsive force on the swimmer. The swimmer moves forward by overcoming the longitudinal viscous drag. The swimmer dynamics is modeled within the framework of slender body hydrodynamics. The model predictions match within 10 percent of the experimental observation. The future potentials of such biological machines will be discussed.