A rotary positioning structure is disclosed for a frame. The frame comprises a housing and a spindle hole disposed on the rear of the housing. The rotary positioning structure comprises elastic members and a rotary stand. Each of the elastic members comprises a tenon and the elastic members are arranged on a circular path surrounding the spindle hole. The rotary stand comprises a rotary shaft and a groove. When the rotary shaft is inserted into the spindle hole, the groove engages with the tenon so that the housing is supported in a first upright position by the rotary stand; also after said rotary shaft is inserted into said spindle hole and then the rotary stand is pivoted on the rotary shaft, the groove engages with another tenon of the elastic members so that the housing is supported in a second upright position by the rotary stand.