Is it true that people can get arthritis (in their fingers) from cracking their fingers?

No. This is an old wives tale. Cracking your fingers does not cause any damage.
Unlikely to happen. Cracking a joint moves the parts of the joint, with the cracking noise coming from cartilage surfaces sliding, from movement of a little air-space from one place in the joint to another, or from some other non-traumatic event. A person with no joint pains before or after cracking a joint is probably not damaging the joint. However, making it a frequent habit has uncertain long-term effects.