Results seem to be mixed, some studies show a positive effect, others no effect at all. The studies referenced by Arthritis Research suggest that going vegan seems to show better results than being vegetarian. Going vegetarian or vegan may have the additional benefit that you're more likely to lose weight over time which will put less strain on your joints. Most studies don't really run long enough to prove this though.
On the other hand, I suppose it's only fair to point out if you are thinking of becoming vegetarian and vegan solely for the above reasons that there is also evidence that the consumption of oily fish can improve the symptoms of rheumatoid arthritis.
On balance,According to changing your diet probably won’t have as great an impactarthritisresearchuk.org, "On balance, changing your diet probably won’t have as great an impact on your arthritis as the medicine prescribed by your doctor will."