I had my little sister take a picture of me.

Literal

I [topic-は] little-sister [by-に] photo [object-を] take-[have-done-てもらった].

Standard benefactive: 撮ってもらう = 'have (someone) take (a photo for me).' に marks the agent of the action being received. 妹 ('younger sister'). A typical family photo scenario.