Add padding to bordered paragraph

"Cell padding" as such does not exist in Word, but you can try these: (I have Word 2007 2010 for Windows right now, but the commands should be similar)

• Open Borders and Shading dialog (Ribbon -> Home Tab, Paragraph sub tab, click on the arrow near the "Borders" icon)
• Click on "Borders and Shading"
• Click on "Options..."
• Adjust the values in "From text"

For the left and right "padding" the "Left Indent", "Right Indent" and "Hanging Indent" handles in the ruler may help (View Tab - > Show/Hide -> Ruler if the ruler is not visible)

(Unable to upload images from my workplace. Will upload from home later today)

Edit: Added images (realized after 3 years, screenshots from Word 2010, instructions pretty much the same)