A novel magneto-optic sensor with electrically adjustable sensitivity is proposed that is based on the approximate multiplication correlation between the linear electro-optic phase retardation and the Faraday magneto-optic rotation angle in a single bismuth germanate crystal. The measurement sensitivity and its temperature stability, linear and monotonic measurement ranges of the proposed sensor can be controlled in real time by adjusting the modulating voltage applied to the sensing crystal. In particular, the proposed sensor can be used for the precise measurement of dc magnetic field or dc current. The basic sensing performance is theoretically analyzed and experimentally demonstrated by dc current measurement.