Kannst du dich bitte darum kümmern?
Since it is literary translated as:
“can you you please about-it to take-care?”
I was wondering what the function of dich here is?
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"Sich kümmern" is a reflexive verb, and therefore is conjugated as "du kümmerst dich" in the second person. The order of words in your case is different due to the sentence structure for questions in German. For a conjugation of reflexive verbs see this resource for more information. This resource provides some more insight into reflexive verbs used in questions.