If you have a spinal cord injury can you walk or move arms?

It depends: It depends on the severity and location of the injury.

Difficultly : If you have a significant spinal injury, usually symptoms are weakness, and sensory loss below the level of injury as well as bowel/bladder problems.

Depends: It would depend on the type of injury and where in the spinal cord (neck, thorax, lower back) the injury occurred. Generally any motor function below the level of injury will be what's affected.

Yes they can: Typically, when one talks about a spinal cord injury most people automatically assume some degree of paralysis in multiple limbs. There are degrees of injuries depending upon severity and location. There is a classification system for people suffering SCI of "E" whereby some neurological deficits can be detected below the level of the injury without motor or sensory compromise at all.