The reliance of feedback mechanisms in conventional light-fueled self-oscillating systems on spatially distributed light and intricately designed structures impedes their application and development in micro-robots, miniature actuators, and other small-scale devices. This paper presents a straightforward rheostat feedback mechanism to create an electrically driven liquid crystal elastomer (LCE) self-oscillator which comprises an LCE fiber, a rheostat, a spring, and a mass. Based on the electrothermally responsive LCE model, we first derive the governing equation for the system's dynamics and subsequently formulate the asymptotic equation. Numerical calculations reveal two motion phases, i.e., static and self-oscillating, and elucidate the mechanism behind self-oscillation. By employing the multi-scale method, we identify the Hopf bifurcation and establish the analytical solutions for amplitude and frequency. The influence of various system parameters on the amplitude and frequency of self-oscillation was analyzed, with numerical solutions being validated against analytical results to ensure consistency. The proposed rheostat feedback mechanism can be extended to cases with rheostats that have more general resistance properties and offers advantages such as simple design, adjustable dimensions, and rapid operation. The findings are expected to inspire broader design concepts for applications in soft robotics, sensors, and adaptive structures.