Abseil, or rappel in AmE, means “to descend using a rope”. Is there a word for “ascend using a rope”?
Abseil is of German origin (infinitive: abseilen). The German antonym would be aufseilen. Since aufseil has not made it into the English corpus, use ascend which is also the translation that fits best for aufseilen. The device used for this action is called an ascender - as has been pointed out in the comments already.