I'm using 2010, so things may be different.
I went to the Data tab, then to Link Data to Shapes. This brings up a box for selecting where your data is from. These are the options:
Excel, Access, MS SharePoint, MS SQL, or Other OLEDB or ODBC.
So I'm not sure if you can actually use Word unless you write your own VB code. Can you bring it into Excel?
After this, in Excel, You can set up your columns of data and use this information to link to your shapes. You may have to edit your shapes Tag so that "Example Column Name" from Excel can link to "Example Column Name" in your Visio tag.