Make your parents think you are being left out, and discriminated by your lack of social network. Tell them it's an easy way to chat with your friends, and give them photos and such.
Your parents are most likely worried about 2 things: 1.) Getting obsessed 2.) Getting stalked.
Most parents believe that if there kid gets a Facebook, they will be all over it, all night, so my advice is for the next week or so, don't go on the computer so much, and make them think that you can handle a new thing.
Stalkers are also why most parents don't let their kid get a Facebook. However, stalkers can't view your page. Facebook automatically has it set that only friends can view any of your info, but you can also set that nobody can search for you either (you have to add people first).
Facebook is fun, helpful, and safe. The biggest thing is don't bother your parents about it too much. Act responsible around the house, and sooner or later, they're bound to let you get one. Most importantly, don't make one without their permission, otherwise, when they find out, they will take it away, and then you will never get one back.