Do you have a Canadian driver’s licence? You can use that instead of the SIN number for the credit check. https://www.koodomobile.com/en/help/credit-check-requirements

It should be noted that you need a Canadian credit card to get a plan online as well. Otherwise, you need to either get a postpaid plan at your nearest Koodo store or get a prepaid plan online instead. 

If you are a permanent resident, you have a SIN number. If you are a guest in Canada (welcome!), then your only option is prepaid, as Milkyway pointed out.

I would suggest you'd look into Public Mobile if that is the case, they have some great offers currently.

When you are trying to order online, is the SIN number mandatory? 

If so and you have the other required ID then you may need to sign up instore