Nope. No bones in the human body can regrow. Yes they can repair themselves, as long as you stick the two peices back together. Kind of like gluing a piece of wood together. But, if you're missin half the wood, it's going to stay missing forever.
Actually, on the contrary. In many cases a rib has been removed and, as long as it is completely removed and the periosteum is intact, it WILL regrow. here is an example from the National Institutes for Health where a rib is removed, used in crainioplasty, and the rib regrows completely : http://www.ncbi.nlm.nih.gov/pubmed/7332200