Hello,
I am Canadian and I've worked at CIBC for 12 years. I actually do credit card applications in my job. I submit the application and then Visa Centre determines if it's approved or declined. "Technically" your supposed to be a PR... however, if they don't know this, it may get approved. We ask for your income and your household income. If you are a "homemaker" then we will use spousal income. If it doesn't approve then you could get a secured card... deposit $500 for a $500 limit. Once you have a card, within a year, you will be approved for any card you'd want.
My husband is a US citizen with not so good credit history... we got him a card through Capital One... secured with $300 and got a $300 limit. It hasn't even been a year and that $300 limit is now $1500 and was offered $10000 at CIBC. So it is possible... and our PR app isn't even submitted yet!!!
BTW, stay away from "store" cards... in Canada they are always close to 30% interest... and they're not considered good credit to have.
Hope this helps.