There isn't exactly an elbow transplant, but an elbow replacement is possible. Most orthopedic surgeons who do elbow joint replacements will consider you for this operation if you meet certain requirements:
You've tried at least six months of nonoperative treatment such as drugs or physical or occupational therapy. Some patients also try acupuncture, nutritional supplements, and other alternative treatments.
Pain does not respond to any nonoperative treatment.
Pain limits motion and function.
There is a fixed flexion contracture (you can't straighten your elbow)
There is nerve damage.
Not all surgeons perform elbow joint replacements. Start by talking with your rheumatologist or other primary care physician. If you have already tried other forms of treatment, ask for a referral to an orthopedic surgeon who does this kind of surgery.