Tendonitis, of any kind, can be helped with acupuncture because of acupuncture's amazing anti inflammatory abilities. 

Muscles attach to tendons and tendons attach to bone. In my experience, tendonitis usually happens when a muscle has been tight for a extended period of time and starts pulling on the tendon.  This pulling causes inflammation and pain.  

Acupuncture and trigger point release can soften the muscle and allow it to return to it's full extension. For example, golfer's elbow, is when the flexor muscles of the forearm get too tight and cause pain at the elbow.  Releasing the trigger points in the forearm followed by rest will greatly reduce pain.