The injection locking properties of rotary dissipative solitons developed in a closed traveling-wave field-effect transistor (TWFET) are examined. A TWFET can support the waveform-invariant propagation of solitary pulses called dissipative solitons (DS) by balancing dispersion, nonlinearity, dissipation, and field-effect transistor gain. Applying sinusoidal signals to the closed TWFET assumes the injection-locked behavior of the rotary DS; the solitons' velocity is autonomously tuned to match the rotation and external frequencies. This study clarifies the qualitative properties of injection-locked DS using numerical and experimental approaches.