The viscosity of magnetic fluids consisting of iron oxide nanoparticles, water, and glycerol has been studied under the conditions of a rotational flow in the presence and absence of a magnetic field. The magnetic field increases the fluid viscosity by 20-80 times. The concentration dependence of the relative viscosity on the magnetic field is described by a curve passing through a maximum. The magnetic field with the lines oriented perpendicularly to the rotor-rotation axis increases the viscosity of the fluid much more strongly than it does with the lines parallel to the rotor-rotation axis.