We demonstrate that a rotating magnetic field can be used to apply a controlled torque on superparamagnetic beads which leads to a tunable bead rotation frequency in fluid. Smooth rotation is obtained for field rotation frequencies many orders of magnitude higher than the bead rotation frequency. A quantitative model is developed, based on results from a comprehensive set of experiments at different field strengths and frequencies. At low frequencies (<10Hz), rotation is due to a small permanent magnetic moment in the bead. At high frequencies (kHz-MHz), the torque results from a phase lag between the applied field and the induced magnetic moment, caused by the non-zero relaxation time of magnetic nanoparticles in the bead. The control of torque and rotation will enable novel functional assays in bead-based biosensors.