I'm also an international student and I've gone through the co-op
process before. You don't need a SIN Card until you actually have a
job. However, you should have applied for your work permit as soon as
you got the letter from the co-op office.
Once you have a co-op job, go to the nearest Human Resources and Skills
Development Canada (HRSDC) office and apply for a SIN card. If you
carry your offer letter with you, they can have the SIN ready by the
next day but the card takes up to 10 business days to arrive by mail.