Coined (probably first in French) from Greek daktylios, finger ring, from daktyl, finger. Per Wikipedia, there's a couple ways the divination works, but all boil down to suspending the ring as a pendulum, and where it points as it swings is read. Bonus word:
dactyliology (dak-ti-lee-OHL-uh-jee) - n., the branch of archeology dealing with gem engraving; the branch of archaeology dealing with finger rings.
Gem engraving because that's how signet rings were made.