In order to study the rotational motion of a vortex ring or the locomotion of bacteria, which propel their cells by rotating their long curved filaments called flagella, the low‐Reynolds‐number flow resulting from the rotation of a torus is studied. The velocity field is obtained by distributing uniform rotlets along a circle with the rotlet directions tangent to the circle. It is found that the effect of curvature of this ring distribution of uniform rotlets is to displace this rotlet ring from the center of the cross section toward the outside of the torus in the normal direction. The net force exerted on the surrounding fluid by the rotational torus is zero. The net torque acting on the fluid is also zero.