Do I have to go to the doctor with a rotator cuff injury?

Not always. Depending on how you injured your rotator cuff, a trip to the doctor may not be necessary. A fall or trauma may cause a full rotator cuff year, which will not heal without surgery. Otherwise, ice, rest and anti-inflammatory medications should make your shoulder fell better within 6 weeks. If not, go see a board certified orthopaedic surgeon for evaluation and treatment.
See a doctor. If you have persistent symptoms of pain that don't respond to rest and nsaids, or if you have sudden onset of weakness or progressive weakness, i recommend you consult with an orthopedic surgeon.

Related Questions

Can I not go to a doctor, with my rotator cuff injury?

You could but should. Not as early DX means early treatment and early recovery from it. Delayed treatments can produce suboptimal results as well. So see your orthopod. Read more...

What would doctors recommend to help with rotator cuff injury?

Rehab. Parital rotator cuff tears or rotator cuff tendonitis is generally treating with nsaids and physical therapy/rehab exercises. You can google rotator cuff rehab exercises for many good ideas. If you have a full-thickness rotator cuff tear, or a large partial-tear, then surgery is usually required. Read more...
Anti-inflammatories. Anti-inflammatory medications and physical therapy may be indicated. See an orthopedic shoulder specialist, who can determine the best treatment plan for you. Read more...