In most cases yes you should be able to register a car with a bill of sale provided you have the bill of sale along with a notarized statement and a receipt proving purchase of the vehicle.
You will then apply for a bonded vehicle title with the bill of sale.
If you've lost the title to the vehicle and the title has already been transferred into your name then you can simply apply for a lost title and pay a lost title fee to get a duplicate title to the vehicle.