To repel is (1) to ward off or drive back, (2) to cause aversion or distaste, or (3) to present an opposing force. To rappel is to descend a vertical surface, especially a cliff face, by sliding down a rope with a device that provides friction. The words are easily mixed up, and the misuse of repel in place of rappel is especially common.
Examples
For example, these writers use repel where they mean rappel:
The team has to repel down what seems to be a massive opening in the Earth’s surface … [Film.com]
That includes a vertiginous Ben Foster, who reluctantly decides to join the eager Statham in a sequence in which both repel down a 45-storey building. [National Post]
These writers use rappel correctly:
Then hikers leave the trail and go down a gully, rappel down a cliff, cross a creek and hike another 150 meters to get to the base of the climb. [Cody Enterprise]
There is no amount of money you could pay us to rappel off of a giant glass building. [Westword]
And these writers demonstrate correct usage of repel:
Commander of Iran’s Army Major General Ataollah Salehi says the army will powerfully repel any possible attack against the country’s sovereignty. [Press TV]
Gottlieb said boy-oriented packaging, even if the customer soon discards it, carries an enduring message that may repel girls. [Monsters and Critics]
Repel has a separate set of issues, particularly when contrasted with repulse, but we won’t get into that here.

