My father glanced at me with an angry face.

Literal

Father [topic-は] angry face [object-を] did [then-て] me [object-を] briefly looked.

怒った顔をして uses a relative clause (怒った) modifying 顔, then をして as a te-form adverbial — 'making an angry face.' ちらっと見る means 'to glance briefly' — ちらっと is a mimetic for a quick, fleeting action.