You'll probably need to use some trial and error to get the rectangle to look natural with the existing table borders. If you don't want to get rid of the fill color, you'll need to move the rectangle so it is behind any text in the document. You can adjust the properties of the drawing object so that the line weight is the same as the table borders and so that there is no fill color inside the object. Then, use the drawing tools in Word (available on the Drawing toolbar) to draw a 'rounded rectangle' around the table. You can then adjust the table borders so that the interior cell borders are the way you want them, but there is no exterior border on the table. Start by creating your table as you normally would.
There is no way to do this directly in Word (tables, with borders turned on, use square corners around the outside edges), but there is a workaround that will work with tables that don't extend past the bottom of the page. Robyn is looking for a way to create a table that uses a rounded border for the outside of the table.