Sensing ultra-low magnetic fields has various applications in the fields of science, medicine and industry. There is a growing need for a sensor that can be operated in ambient environments where magnetic shielding is limited or magnetic field manipulation is involved. To this end, here we demonstrate a new magnetometer with high sensitivity and wide dynamic range. The device is based on the current nonlinearity of superconducting material stemming from kinetic inductance. A further benefit of our approach is of extreme simplicity: the device is fabricated from a single layer of niobium nitride. Moreover, radio frequency multiplexing techniques can be applied, enabling the simultaneous readout of multiple sensors, for example, in biomagnetic measurements requiring data from large sensor arrays.