Until you are a permenent resident, you probably won’t be able to register your car until you import it. When you do get your PR, there are guidelines to follow in both Canada and the US. Your car will need to be on the RIV list of vehicles eligible for entry to Canada. You will need to make sure any recalls are completed and you have proof from the manufacturer they are done. You will have to export the car from the US and then import it to Canada. If the value is over $10K, you will need to pay tax on the value above that amount. Once I’m Canada, you will need to have it inspected and brought up to Canadian standards. Only then can you register it. More info here:
https://www.tc.gc.ca/eng/motorvehiclesafety/safevehicles-importation-usa-index-445.htm
https://www.riv.ca/ImportingAVehicle.aspx
https://www.cbp.gov/trade/basic-import-export/export-docs/motor-vehicle
It all sounds like a hassle, but it’s not that bad. Depends on where the car was made and how old it is. If it’s an older car, it may not be worth it after the inspections and repairs that may be required.