Hi jerseylady1, welcome to the forums.
Do you mean that you want to connect to Facebook like you would through the internet? If so, then yes there is a built in web browser, but it is not very good.
Do you mean that you want to connect to Facebook so that you can post reading quotes and comments from within the books you read? Then the answer is yes. You need to go into the settings and set up Facebook and/or Twitter account information first. You can then quote books directly into Facebook and/or Twitter.
Here is the link to Amazon's instructions on how to
link your Kindle to Facebook or Twitter.