Well, the first thing you need to establish is who was at fault. If you, the bicyclist, were at fault in causing the accident, then no, you cannot sue the driver. However, if the other driver was at fault in causing the accident by acting negligently or carelessly, then certainly you have a claim or a lawsuit that can be brought against them.
One other thing that can be kept in mind is, you don’t have to go right to a lawsuit or suing them. There is a potential of settling the case out of court directly with their insurance company before going as far as a lawsuit.