Tied or bound with rope, or tricked into doing something you didn't want to do.
From Old English 'rap,' a noun meaning rope. The verb form developed naturally when the noun was used as an action word—'to rope' someone or something.
Getting 'roped into' something comes from the literal image of being bound by rope, but now it's almost always metaphorical—a perfect example of how concrete actions become abstract ideas in language.
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