A 1-mm-size cluster composed of 10 dust particles immersed in plasma is rotated by the torque of a pulsed electron beam with energy in the range 8-12 keV. The dust particles are electrically charged spheres with radius 5.9 μm and are levitated in the plasma sheath, forming a round, planar, Coulomb-coupled cluster. The electron beam irradiates the dust cluster passing slightly off its center, and sets the particles in motion by the action of the electron drag force. The total torque at 12 keV is 4.9±0.2×10^{-11} Nm at an angular speed 1.41±0.05 rad s^{-1}. The main dynamical features of the cluster such as intershell rotation and itinerancy of the dust particles inside the cluster are simulated by using a molecular dynamics code.