Joseph Germanotta apparently ordered the drink over the phone with HeadQuarters strip club in New York on Monday where GaGa would later be partying.
However, employees were sceptical of his identity, reports the New York Post.
"The staff at first didn't believe it was GaGa's dad," a source said.
"They asked for his credit card number three times and Googled him before they took his order."
GaGa is said to have later appeared at the club wearing only "a transparent jumpsuit with a few carefully placed sequins over her nipples and private parts".
