Not the expression, no, literally give an arm for?
“I would give my right arm” is a common expression that implies that the person would do absolutely anything. In this case, he’s talking about love.
Other expressions that people say (in this case) include, “I’d take a bullet for you…” along with cheesy lines like:
Em is willing to literally sever his arm for Hailie
Eminem has a picture of Hailie tattooed on his arm, so he “gives” that arm to her
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