Giovinazzo, 39, was pulled over after officers spotted him driving his Jeep Wrangler erratically early Jan. 21, TMZ reported Wednesday.
Police said the actor smelled of alcohol, had bloodshot eyes and was slurring his speech.
Giovinazzo was arrested for suspicion of DUI after he admitted drinking scotch at the W Hotel and his blood alcohol content registered at almost twice the legal limit.
The arresting officer told TMZ the actor "repeatedly apologized to me and told me he didn't want to be an [expletive.]"
"[Giovinazzo] thanked me many times for not treating him like a criminal and showing him respect," the officer told the celebrity news website.
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