The Troy star is appearing in Conor McPherson's show at London's Donmar Warehouse, but he halted his performance after hearing noise from the audience.
A source tells the Daily Mail: "It was a very intense moment and this phone kept ringing. Everyone was cringing and praying it would stop but it went on and on. Finally, Cox flipped and said menacingly, 'Please just stop it, whoever it is, just stop it!'"
The publication reports a woman in the audience quickly silenced her phone, and Cox continued with his performance.
Earlier this month, fellow Scottish actor James McAvoy also broke character during his performance of Macbeth to berate a theatregoer for filming the play on a mobile phone.