Yes you can: As a student at the gibb you can register for a Cambridge exam directly with the following link for Cambridge English Examinations Centre Bern.
First, choose your exam, register as an individual, then add your personal details and gibb department and finally follow the payment instructions. There is a complete list of all other exams currently available for registration, free resources and FAQs at the bottom of the gibb registration page. Please contact your gibb English teacher if you have any questions.
Good luck with your exam!