The way a torn rotator cuff is treated is based on what caused the injury, exactly where the injury is, and how severe it is. Your rotator cuff is not one body part, but is really made up of four tendons that help your shoulder move. When one of the tendons becomes injured, this is a rotator cuff injury or a rotator cuff tear.
Small tears or injuries often heal on their own, with treatment such as suggested by your doctor. By not using the shoulder or by not doing the motions that caused the injury, you are resting it, allowing it to heal. By applying ice and taking the medication, you are reducing swelling and pain, which should also help the healing process.
If you feel that your shoulder isn’t healing, you should speak with your doctor to see if it is, but you don’t see it/feel it, or if you need a different treatment approach.