We lay the theoretical basis for one-bead microrheology with rotating particles, i.e., a method where colloids are used to probe the mechanical properties of viscoelastic media. Based on a two-fluid model, we calculate the compliance and discuss it for two cases. We first assume that the elastic and the fluid component exhibit both stick boundary conditions at the particle surface. Then, the compliance fulfills a generalized Stokes law with a complex shear modulus whose validity is only limited by inertial effects, in contrast to translational motion. Secondly, we find that the validity of the Stokes regime is reduced when the elastic network is not coupled to the particle.