A study in Britain involving more than 23,000 participants found that people who consumed less vitamin C had a higher risk of developing inflammatory polyarthritis, a form of rheumatoid arthritis that affects two or more joints. Reducing the risk of inflammatory polyarthritis may or may not correlate well with other types of arthritis, but the fact that vitamin C plays a positive role in protecting joints seems obvious.
Of note, a 2004 animal study showed that high levels of prolonged vitamin C intake actually increase the risk of arthritis progression in the knee. Human studies are needed to confirm or refute these results, but this does offer an argument to not exceed the recommended daily allowance (RDA), which is 90 mg for men and 75 mg for women. Because of this somewhat conflicting evidence, I do not recommend vitamin C supplementation for arthritis.