A prophecy is (1) a prediction of the future, or (2) a revelatory utterance. The word is only a noun. Prophesy is a verb. To prophesy is (1) to predict, (2) to reveal by divine inspiration, or (3) to speak as a prophet.
Examples
Prophecy
If the West does nothing, then Carney’s prophecy will be self-fulfilling. [Winnipeg Free Press]
Alfonzo’s prophecy didn’t seem plausible at the time: oil made every petro-state ruler a Midas. [Telegraph]
As with Orwell’s classic, the lines between social commentary, satire, dystopian prophecy and a hopefulness of spirit are often deliberately blurred. [Sydney Morning Herald]
Prophesy
Tony Parker aside, I hold that it’s still too early to prophesy about the Lakers’ playoff situation. [comment on Los Angeles Times]
That hardy media staple, the “summer of discontent”, so often falsely prophesied, may finally come to pass. [Financial Times]
Back in 1982, the gravelvoiced media studies professor prophesied “the disappearance of childhood” in a book of the same name. [Vancouver Courier]