네가 뭔데 날 이렇게 홀려놔? = 네가 무엇인데 나를 이렇게 홀려 놓아?
=> 네가(you) 무엇인데(are what) 나를(me) 이렇게(like this) 홀려(enchant, enrapture) 놓아(leave, put)?
=> Who are you to enrapture/enchant me like this?
It's most likely saying "You have (romantically) enraptured me so completely, which is unfair.", an irony-tinged protest directed to the person who has captivated her, along the lines of "You stole my heart. I want it back" often heard in songs.