。
She smiled at me.
Literal
She [topic-は] me [to-に] smiled-toward.
微笑みかける is a compound verb (微笑む 'smile' + ~かける) — the suffix ~かける here means 'direct (an action) toward' rather than 'be on the verge of' (its other major sense). 話しかける ('speak to'), 呼びかける ('call out to'), 問いかける ('pose a question to') all share this directional ~かける. The に marks the speaker as the target of the smile. The construction makes the directionality of the smile explicit: it wasn't just a smile in general, but one aimed specifically at the speaker.