Miniature inner grooved copper tube (MIGCT) is widely applied in industries. To overcome the weak rigidity and strength of MIGCT during stepped tubes manufacturing, rotary swaging process was selected after comparing with radial forging process. The working principle of the rotary swaging was analyzed. A rotary swaging machine, whose workpiece feeding and clamping was respectively driven by an air cylinder and a finger cylinder, was designed. Experiments indicate that the MIGCT was slave rotating with forging dies during rotary swaging. Theoretical analysis was done to investigate the reason of the slave rotation. Experiments were carried out to verify the theoretical analysis. Furthermore, the influences of push force and clamping force on rotation speed were discussed. With the increase of clamping force, the rotation speed of MIGCT decreases gradually in a constant ratio. However, the push force influences the tube rotation speed slightly. In general, it found that an optimal rotation speed of MIGCT is beneficial to the manufacture of the stepped tube.