Impairment of hand functions in individuals with spinal cord injury (SCI) severely disrupts activities of daily living. Recent advances have enabled rehabilitation assisted by robotic devices to augment the residual function of the muscles. Traditionally, electromyography-based muscle activity sensing interfaces have been utilized to sense volitional motor intent to drive robotic assistive devices. However, the dexterity and fidelity of control that can be achieved with electromyography-based control have been limited due to inherent limitations in signal quality. We have developed and tested a muscle-computer interface (MCI) utilizing sonomyography to provide control of a virtual cursor for individuals with motor-incomplete spinal cord injury. We demonstrate that individuals with SCI successfully gained control of a virtual cursor by utilizing contractions of muscles of the wrist joint. The sonomyography-based interface enabled control of the cursor at multiple graded levels demonstrating the ability to achieve accurate and stable endpoint control. Our sonomyography-based muscle-computer interface can enable dexterous control of upper-extremity assistive devices for individuals with motor-incomplete SCI.