The drugs – 0.04g of cocaine with a street value of about £3 – were found in a bag in a glove compartment.
Ahmad Zeidan, 20, claimed he was tortured into signing a confession after being arrested in December.
He denied the drugs belonged to him and said the confession document was in Arabic, which he did not understand.
Zeidan was studying at the Emirates Aviation College in Dubai at the time of his arrest.
He claimed he was in a car with men he did not know well when the drugs were found.
Following his arrest, he alleged he was held incommunicado for several days, was hooded, beaten and threatened with rape.
The justice charity Reprieve said it had uncovered evidence of a systematic pattern of torture in UAE prisons and had sent a dossier to the UN special rapporteur on torture on behalf of 19 prisoners.
Kate Higham, a legal investigator at Reprieve, said: "The UAE must urgently reconsider Ahmad's case, while the British government must do all it can to push for his release."
A Foreign Office spokesman said: "We are aware that a British national has received a custodial sentence in the United Arab Emirates. We are providing consular assistance."
A student from Reading has been jailed for nine years in the United Arab Emirates for possessing cocaine worth less than £5.