The observational data on torsional oscillations of magnetic and velocity field vector components of seven single sunspots are studied. It is found that the period of sunspot torsional oscillations increases with the increase of the solar rotation period calculated with the use of these sunspots. The oscillation amplitudes show the tendency to be larger for the sunspots having a higher latitude. We suggest the excitement mechanism of magnetic flux tube torsional oscillations based on plasma motions in super granulation cells and on the action of the Coriolis force on these motions. The time of formation and decay of the supergranulation cells between which the vertical magnetic tube is situated defines its torsional oscillation period. Amplitudes of oscillation components are calculated. For a radial velocity of plasma motions in supergranules of 0.2 km/s and plasma density of 2 g/m³, the magnitudes of torsional oscillation amplitudes are in good agreement with those obtained from observations.