YES you can become a massage therapist with arthritic hands. You'll want to focus on learning one of the 'Energy Modalities', like Thai Yoga Massage or Shiatsu, both of which utilize more direct pressure with the feet, arms, legs and palms of the hands : while requiring less rubbing motion with the hands.......or maybe even the modality of 'Back Walking', where you won't need to use your hands for anything at all but to balance yourself..........or even Reiki where your hand barely if rarely even toughs the clients.
Look to work with one of the councilor at a School of Massage to find one of the many modalities of massage that fits your personality & situation the best.