While there is no absolute age at which scary movies are appropriate, Dr.Dry recommends not introducing them to very young children because of the potential to create long-term anxiety.
11-13 year olds may be better equipped to navigate the scary movie scene on some level but each child is different. If your child watches something that they say is not scary to them but then starts coming to you at night wanting to sleep closer to you or is having nightmares let their behavior speak for them.