I had a verbal argument with my older sister.

Literal

I [topic-は] older-sister [with-と] mouth-quarrel [object-を] did.

口喧嘩 (くちげんか, 'verbal quarrel') — 口 ('mouth') + 喧嘩 ('quarrel'). 姉 (あね) is the neutral/humble term for one's own older sister (vs. お姉さん). と marks the companion/partner in the argument.