Does an orthopedic surgeon also do cortisone injection therapy?

Yes, also. Rheumatologists also have a lot of experience with joint injections.
YES ! Orthopedic surgeons are experts in joint anatomy and performance. Most of us have seen these joints 'on the inside' during surgery. Injections of many kinds can be given including cortisone. With this experience we often know the easiest most painless and quick way to give an injection when it is truly needed.
Yes. Orthopedic surgeons perform all levels of joint treatment from joint injections of cortisone or lubricants to extensive surgical repair and replacement procedures. Due to the high volume of patients that orthopedic surgeons see they are the medical professionals with the most experience and expertise in joint injection techniques.