Yes, you sure can! For more info on Facebook guidelines, check out our article on Facebook promotion guidelines here and join the conversation!
We released an app that makes it easy to manage a giveaway on your timeline as well called the Facebook Flash Giveaway App.
Here's a description of how the Rafflecopter Facebook flash giveaway app works. If you're running a giveaway on your Facebook timeline, here's an article that describes 5 best practices for your Facebook timeline giveaway.