Technically, you own all of the content you post on Facebook; therefore, you can copyright it. HOWEVER, by posting something on Facebook you:
...grant [Facebook] a non-exclusive, transferable, sub-licensable, royalty-free, worldwide license to use any IP content that you post on... Facebook.
and while this license ends when you delete the content from Facebook or delete your account, this does not apply if "your content has been shared with others, and they have not deleted it."
For practical purposes, this could reasonably be interpreted as meaning that if somebody saves content you shared on FB to their computer, then while you still own the copyright to that content, Facebook has full rights to use that content, as does anyone they choose to sub-license or transfer that right to.
Long story short: You own everything you post to Facebook, but Facebook can do pretty much whatever they want with it, including allowing other people to do pretty much whatever they want with it. Don't post something to Facebook if you want to keep control over who uses it and how.
Source: Facebook Terms of Service