Yes you can!
I recently read a blog post by Michael Hyatt that provides readers with very detailed instructions, including pictures, on linking your Facebook and Twitter accounts. I wish I would have known about this little trick months earlier as I have a hard time switching between and updating both social networks on a regular basis. The process is so simple that it took me a little over a minute to successfully link my accounts.
Be mindful that linking the accounts using Michael’s method allows Twitter to update Facebook with every tweet that is not an
@reply or a direct message. If you wish to have more control over what you want to share on Facebook and want to select the tweets you share then scroll to the bottom of his post on his update regarding “Selective Tweet Status” updates.