Sternocleidomastoid muscle is supplied by:
Vagus nerve
Spinal accessory nerve
Marginal mandibular branch of facial nerve
None of the above
The spinal accessory nerve provides the motor supply. It passes through the muscle.
The spinal accessory nerve supplies:

The sternocleidomastoid, the chin turning
The trapezius, the shrugging muscle.

Cervical nerves provide a proprioceptive sensations to these muscles.
Reference: B D Chaurasia’s Head and Neck anatomy, 6th ed page no 384