drunk dial
v. To make an embarrassing phone call while inebriated.
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Examples
2002
Drunk dialing" brings blushes of recognition. Oh, yes. "Saying things that you shouldn't be saying because the cell phone's in your pocket and you're drunk," someone acknowledges, knowingly. "If you've got the phone in your hand, it's such a temptation."

"Stupid things," says Angie Hacker, an intern with the U.S. Public Interest Research Group. "My best friend at home, she broke up with this guy she went out with for two years. She calls him and like, 'I know you're not over me. I know you feel that way. You're just going out with that other girl because she's around.' And then she hung up.
—Joel Garreau, “Cell Biology,” The Washington Post, July 31, 2002
1997 (earliest)
Have you ever committed a "drunk dial?" (Called someone up when you were drunk and said things you wouldn't say when you were sober?)
—Cheryl Lavin, “Gentlemen, start your engines,” Chicago Tribune, August 24, 1997
Notes
Of the roughly one dozen unique citations I found for this phrase, four were from Cosmopolitan magazine, and a fifth was from a novel written by a Cosmo editor. I'll leave you to jump to your own rash conclusions.