Yes, all residents of BC are eligible for the vaccine. This includes international students in the country.
From the BC Centre for Disease Control:
COVID-19 vaccines are available at no cost to everyone 12 years of age and older living, working or studying in B.C.
If you did not get vaccinated before coming to Canada or need to complete your immunization with a second dose, you will have the opportunity to get vaccinated in B.C.
All students will be eligible to receive the vaccine, including international students and their families. You do not need a Personal Health Number (PHN), B.C. Services Card, or to be enrolled in B.C.'s Medical Services Plan to get the vaccine. However, all students are encouraged to obtain a PHN in order to use the provincial on-line vaccination booking system.
Learn more about the COVID-19 vaccine in BC.