The phrase "accept a cup" is correct and usable in written English.
You can use it when offering or requesting someone to take a cup, typically in the context of serving drinks or refreshments.
Example: "Would you like to accept a cup of tea while we discuss the project?"
Alternatives: "take a cup" or "receive a cup".
She refuses medical care, refuses the police, but will accept a cup of tea, and goes with him to his apartment.
Michelle cannot accept a cup of coffee that has not come from a "cafetière," and strews casual insults around the living room with abandon.
At the open-air hall, he sat onstage, leaning over the microphone, gesticulating with his big hands, denouncing the military council as remnants of Mubarak's regime, and pausing occasionally to light a cigarette or accept a cup of tea.
Red-faced, Ray accepted a cup of boiled custard.
Venerable Kassapa sat at a small table and accepted a cup of decaffeinated coffee.
She accepted a cup from Nazneen and held it in her man-size hands.
The man accepted a cup of coffee – make that a mocha, he said – and $5 from a reporter.
Don accepted a cup, and gulped down the ice water that she had remembered to bring him, but shook his head at the cookies.
At the news conference announcing the indictment, David A. Cardona, head of the criminal division in the New York City F.B.I., pointedly noted that a police officer can face trouble for accepting a cup of coffee.
Known for its strict, by-the-books culture — accepting a cup of coffee from a supplier can be a firing offense — Wal-Mart is now encouraging its merchants to speak frankly, even critically, about the products the chain carries.
The first is to be found in Angkor Wat, where a bunch of orange-clad Cambodian monks are chuffed to meet Lara, despite the punishment she hands out to their national treasures - and she accepts a cup of soothing tea from them.
