The council has permitted a pair of Bactrian camels to be privately owned in Mid Devon, new figures show.
Wildlife charity the Born Free Foundation said improved regulation is needed, after its research found thousands of wild animals are owned privately across Great Britain.
Figures obtained by the charity from freedom of information requests sent to councils reveal there is a dangerous wild animal licence allowing two Bactrian camels to be kept privately in Mid Devon.
Chris Lewis, Born Free's captivity research officer said: "The Dangerous Wild Animals Act was intended to make the keeping of such animals categorised as 'dangerous' a wholly exceptional circumstance.
"However, Born Free’s ongoing research paints a very different picture."
He added regulations on the keeping and trading of wild animals kept as pets are "in urgent need of review".
Across Great Britain, the charity found over 2,700 dangerous wild animals were licenced to be owned privately. They include more than 200 wild cats and 250 primates.
It estimates there are also 400 venomous snakes "kept in British homes", more than 10 times the number in zoos.
The South West was home to several wildcats included lynxes and leopards. Analysis shows the number of reported venomous snakes in the region has almost doubled from 25 in 2020 to 44 last year.
Mr Lewis added regulations on the keeping and trading of wild animals kept as pets are "in urgent need of review".
Dr Mark Jones, the charity’s head of policy said: "It is unbelievable that, in this day and age, so many dangerous animals, including big cats, large primates, crocodiles and venomous snakes, continue to be legally kept in people’s homes in the UK.
"Increasing demand for and trade in all kinds of wild animals as exotic pets puts owners and the wider public at risk of injury or disease," he added.
"It also results in serious animal suffering, and the demand increases the pressure on many wild populations which are often already under threat."
A Department for Environment, Food and Rural Affairs spokesperson said anyone wishing to keep an animal under the Dangerous Wild Animals Act must be vetted and apply for a licence which sets out conditions on caring for the animal.
They added: "We keep this legislation under regular review to ensure it remains effective in keeping the public safe."
They said the Government increased the maximum prison sentence for animal cruelty to five years in 2021, and added it is currently bringing forward legislation to prohibit primates being kept as domestic pets.