Sensing small magnetic fields is relevant for many applications ranging from geology to medical diagnosis. We present a fiber-coupled diamond magnetometer with a sensitivity of (310 $pm$ 20) pT$/sqrt{text{Hz}}$ in the frequency range of 10-150 Hz. This is based on optically detected magnetic resonance of an ensemble of nitrogen vacancy centers in diamond at room temperature. Fiber coupling means the sensor can be conveniently brought within 2 mm of the object under study.