This sensor comprises a magnetic circuit (CM) which comprises an air gap and a device which delivers a voltage (V2) which is representative of a magnetic field generated in the air gap by a current (IM), when this current passes through the circuit. The value of the field is a function of the strength of the current. The device is a directional resonance magnetometer (MD) comprising a sample (2) comprising resonance spins, placed in the air gap and subjected to a polarising magnetic field parallel to the field generated in the air gap or coincident with it, and measurement means provided to excite the resonance and detect the excited resonance, and to deliver the said representative voltage.
