What do you call a person who tells fortunes by reading your hand?

Those who practice chiromancy are generally called palmists, palm readers, hand readers, hand analysts, or chirologists. See: http://en.wikipedia.org/wiki/Chiromancy

The art of scrying by reading the lines, mounts and planes of a person's hand is Palmistry.

A hand-y man?? Nah, most people who work with their hands are manual laborers.

That would be a numerologist .

In the Roman Catholicism: A Lector; since the person reads from a Lectionary. In the Roman Catholicism: A Lector; since the person reads from a Lectionary.