A rotator cuff injury doesn’t preclude one from engaging in physical activity.
Your physical therapist will likely prescribe exercises to help strengthen your shoulder girdle.
Too, one has to take into the degree of the injury. I would wonder whether you have a tear or a rupture. Whatever the case, there is plenty to do other than utilized the injured part of the body.
You should, however, consult with your orthopedic surgeon as well as your physical therapist to determine how you should proceed.
All the best to you.