。
She's angry with me.
Literal
She [topic-は] me [at-に] is-angry [progressive-ている].
怒る ('to get angry') in the ~ている form expresses an ongoing emotional state — 'is angry,' as opposed to the bare past 怒った ('got angry,' the moment of becoming angry). The に marks the speaker as the target of the anger ('at me'). 怒る covers the full range from mild irritation to full fury; the more idiomatic 腹を立てる captures specifically the moment of becoming angry, drawing on the older Japanese metaphor of the belly as the seat of emotion. The ~ている vs past-form contrast is what draws the line between sustained state and the moment of onset.