A hair styling appliance for curling hair, includes a gripping handle along a first axis and a housing having a winding chamber defining a second axis an introduction slot and an extraction opening. The first and second axes form a plane. A barrel has fixed and free ends disposed close to the extraction opening and extends in the winding chamber along a third axis in the plane. The third axis is inclined at an angle with respect to the first axis such that the free end is farther away from the gripping handle than the fixed end. A hollow winder is arranged around and coaxially with the barrel. The winder is mounted to rotate about the third axis and to successively grasp the proximal end of the lock, concomitantly wind the lock about the barrel and the winder, and then completely wind the lock around the barrel, as it rotates.