rhabdomancy: Fortune-telling by rods or wands.
You might recognize the link to magical power that -mancy brings to the word from necromancy or William O. Gibson's Neuromancer. There's also oneiromancy (divination through dreams), hydromancy (divination by water), and a whole mess of others.
Rhabdo- was a new root for me, usually indicating, in some way, "rods." For example, a rhabdovirus is a rod- or bullet-shaped virus, and a rhabdom (a good Scrabble word) is a rod-like internal structure of an arthropod's eye.
I don't think it counts as rhabdomancy if you predict that someone is in danger of being attacked and then immediately start hitting him with a stick. Predictions about Rod Stewart also aren't necessarily rhabdomancy.
Rod Blagojevich could have use a good rhabdomancer.