The thermocapillary motion generated within a spinning vaporizing droplet is described. Rotation induces a swirling flow in the surrounding gas. This in turn establishes a nonuniform vapor concentration and temperature at the droplet surface. An internal circulation is thus created from the interfacial temperature gradients. This internal motion, described in the limits of small Reynolds and Marangoni numbers, appears as a pair of toroidal vortices. Depending on whether the gaseous Lewis number, Le, is less than or greater than one, the temperature along the surface peaks at either the poles or the equator of the droplet. Consequently, the direction of the internal circulation is from the poles to the equator or vice versa.