You can use the Google Analytics API to check for this, with the caveat that if javascript is not enabled OR if the user has taken steps to block tracking by Google Analytics, their data will not show up.
Use the fullReferrer dimension to get the source and referral path (i.e. website name and URL where you can find the link to your site).
You can also use Google Webmaster Tools to see who is linking to your site. Look under Search Traffic > Links to Your Site and you will see the full list. This may help you to find those sites where your publishers have posted their affiliate links.