She called me again and again.

Literal

She [topic-は] many-times me [to-に] phone [object-を] hung-coming.

電話をかける is the standard collocation for 'make a phone call.' The かける ('hang, place, put on') here is the same one you see in 鍵をかける ('lock'), 眼鏡をかける ('wear glasses'), 声をかける ('call out'). Adding ~てくる ('motion toward speaker') to かける gives かけてくる: the call comes toward me, the speaker. Pair it with 何度も ('many times') and the repetition reads as a barrage — possibly affectionate, possibly annoying, possibly desperate, depending on context.