If you decide to give up gluten, rheumatoid arthritis shouldn't be the reason. There's no evidence that it can improve the condition or ease your symptoms.
Gluten is a protein found in wheat, rye, and barley, and in many packaged and restaurant foods. If you have celiac disease and eat gluten, your small intestine gets inflamed, so you can't absorb some nutrients. Rheumatoid arthritis is separate from that, and it has different causes.
If you want to ditch gluten, talk to your doctor or a dietitian for tips so you get all the nutrients you need.