Susan,
If you have a Facebook Fan Page, you should be using Facebook Insights which provides statistics on engagement. It can't tell you how many total visits you have to your page but you can measure the growth of your community based on Fans gained. Remember, building and engaging community is key if you are to try to use social media as a tool to drive outcomes. You must first have a community and they must be engaged before you can design ways to try to drive outcomes that align with your career center objectives. The ideas are limited only to your imagination on what you will try to experiment with to drive the desired outcomes (such as more student one-on-one appointments, more event participation, job leads sourced by word-of-mouth from the community sharing what they have found, increased student awareness of the services you offer, etc.)
Robert Starks Jr.