We demonstrate the controlled rotation and torque generated by uniaxial magnetic microactuators formed by two bound superparamagnetic particles in a fluid. The torque and rotation are precisely controlled by rotating magnetic fields, generated by an external electromagnet or by on-chip current wires. We present the magnetic energy equations and the equations of motion for two-particle microactuators, with contributions from the permanent and induced magnetic moments of the particles. A comparison of theory and experiments allows an estimation of the different moments with accuracy better than 10% across a wide frequency range. At low frequencies and low magnitudes of the applied magnetic field, both the permanent and induced moments of the particles have contributions to the torque. At either high fields or high frequencies, the torque is dominated by the induced moment. The predictability of the torque is highest in the regime of low frequencies and high field, where the torque has a large magnitude and is determined by the magnetic shape anisotropy of the microactuator. A comparison of rotation in bulk fluid and on a chip surface shows an increase of friction by a factor 9 originating from the surface proximity. The detailed understanding of the torque and rotation of two-particle uniaxial magnetic microactuators opens a range of possibilities in lab-on-a-chip applications, such as the actuation of single molecules, fluid mixing in microfluidic chambers, and novel cluster-based assays.