Although I do not have arthritis I exercise my fingers before playing a lot. They are basic stretching exercises and the first one includes doing "push-ups" with my index finger, similar to when you were a kid and did finger puppet movements (at least I did). I even saw a book on Mel Bay once about finger exercises for instrumentalists. I bet you can find something on the web. I also use a finger exerciser and I will post what it is called later. My exercises have all been as preventative measures and not restorative, so they may not help.

I also rub wintergreen isopropyl rubbing alcohol on the joints and the tips of my fingers before playing and sometimes afterwards.

Just a poor lame joke (sorry I could not resist):

Instead of playing guitar with Art Hritis play guitar with Art Thieme (a legend on Mudcat)

Good luck and continue to exercise and warm up before playing.