Marco Pierre White Jr, 21, had pleaded guilty to dishonestly making a false representation on 23 November.
He was told he had to undertake 120 hours of unpaid work and pay £2,500 in compensation to his victim.
Chief magistrate Emma Arbuthnot said she believed goods he had bought with the money were "sold to buy drugs".
"There is no doubt this is serious enough for a community order," she said while also admonishing Pierre White Jr for "smirking" in the dock.
Westminster Magistrates' Court heard the former Big Brother contestant admitted making a "high volume" of payments on Carina Evans's card after borrowing it to buy food in February.
When the card was blocked, he tricked Ms Evans into unblocking it by pretending he had been arrested and needed to pay bail.
He then went on to spend about £2,500 during visits to shops including the Apple Store and Sunglasses Hut.
He previously pleaded guilty to dishonestly making a false representation at Hammersmith Magistrates' Court.
The son of chef Marco Pierre White has been ordered to perform unpaid work after he admitted dishonestly using his ex-girlfriend's bank card.