1. Go to this site: http://www.systemrequirementslab.com/cyri/
using either Internet Explorer or Google Chrome (since it requires ActiveX support) and make sure the browser you're using isn't blocking the plugin.
2. On the drop down, find "Star Wars: The Old Republic" (it's the last Star Wars title on the list)
3. Click "Can you run it?" and wait for the results.