She treated me to a cup of tea.

Literal

She [topic-は] me [to-に] black-tea [object-を] one-cup treated [for me-てくれた].

ふるまう (振る舞う) means 'to treat (someone to food/drink), to entertain,' in the sense of offering hospitality. Distinct from ごちそうする (also 'treat to a meal'), ふるまう often suggests a more spontaneous or casual offering — pouring a cup of tea, putting out snacks. 紅茶 ('red tea,' or English-style black tea) is the standard distinction-word from 緑茶 ('green tea') and お茶 (often defaulting to green or just 'tea' generically). The counter 杯 (はい/ぱい) is for cups, glasses, and bowls of liquid — 3杯 (さんばい), 6杯 (ろっぱい) with euphonic changes.