Rappel, in general, describes the maneuver of descending vertically via rope.
Is there a single word that describes the opposite action of being pulled directly upward or ascending vertically via rope?
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hoist, Merriam Webster
to raise into position by or as if by means of tackle: hoist a flag; hoist the sails; Cargo was hoisted up into the ship.
Example (made up):
Clinging to the rope, she was hoisted up the side of the ship by the burly sailor.
In the question, The OP speaks of being pulled directly upward, and in a comment, the OP says being pulled upwards by some outside force (mechanical or otherwise, doesn't matter). Not climbing. Hoist fits these specifications.
But the OP also said, in the question, ascending vertically via rope. For this, the comment of @Lambie to prusik would fit, but the OP said not climbing. So the question needs clarifying. (I will leave it to Lambie to give the prusik answer.)
If you are OK with implying the use of a mechanism in addition to the rope, you could use the verb winch. From MacMillan Dictionary:
to lift someone or something using a winch
a piece of equipment that uses a rope or chain for lifting or pulling things or people
So you could say, for example,
Clinging to the rope, she was winched up into the helicopter.
And if you just said
The rescue helicopter winched her out of the water.
it would be clear that you meant that she was lifted via some sort of cable.
However, if you want to use it in a situation where there is a single person hauling the rope (with passenger attached) hand-over-hand, I think you'd need to use a different verb and specify the rope.
The opposite of rappel is ascend. The device is called an ascender. (Wiki article lists some alternate/obscure names for ascending.)
The action of climbing is very different depending if you are climbing a wall using a rope, or climbing a rope with nothing for support. Either way, I would say "climb". I'm not sure if there is a word for using a mechanical device that pulls you up a rope, because I'm not sure if they exist in real life.