Arthritis Self-Management reports that honey and cinnamon have not been scientifically proven to treat arthritis. Additionally, the Arthritis Foundation does not list honey or cinnamon in its list of supplements and herbs known to treat arthritis.
Both Arthritis Self-Management and Snopes.com note that the original article claiming that arthritis could be treated in this way is found in the "Weekly World News," a tabloid publication. They mention that the original article referenced a study at the University of Copenhagen, but no such study exists. Wikipedia articles for both honey and cinnamon state there is little scientific evidence for the medicinal properties of both substances even though they have been studied in clinic trials.