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.

Fighting is said to have erupted near the town of Harad which was captured by government forces two days ago.
Military sources said 28 troops were killed while Houthi rebels said they had lost 40 fighters.
Clashes have continued despite a UN-backed ceasefire and peace talks in Switzerland which began on Tuesday.
As well as those killed on Saturday, at least another 50 rebels and 40 pro-government troops were reported to have been wounded.
Tribal sources said there was an upsurge in fighting early on Saturday as government forces - which are being backed by a Saudi-led coalition - advanced towards the Red Sea port of Midi and rebels brought in reinforcements.
Houthi and government delegates have been meeting in Biel in Switzerland to try to end months of fighting.
Rebels have accused Yemeni and Saudi-led coalition forces of repeatedly breaching the ceasefire, which is meant to last for a week.
The Saudi-led coalition launched a military campaign in March in support of the government after Houthis seized the capital, Sanaa, and advanced towards the second city of Aden.
Since then, at least 5,700 people, almost half of them civilians, have been killed in air strikes and clashes on the ground.
The humanitarian crisis in Yemen has also worsened, with more than 21 million people - four-fifths of the population - now in need of aid.
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.
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At least 68 people are reported to have been killed in fresh clashes between government troops and Houthi rebels in north-west Yemen near the Saudi border.