To restrict your referral program so only customers who have previously ordered from you can send referral in your Magento store:

  1. Login to your Magneto admin.
  2. Go to System (top menu) > Configurations (sub menu) > Refer A Friend (left menu)
  3. Find the Require Purchase section and update the drop down box to say Enable to require customers to have made at least one purchase before they can send a referral. 
  4. You'll also want to review the message to show to customers if they try to refer without having made a purchase from you previously. Go to CMS > Static Blocks > search "purchase" under Title > click on Refer A Friend Purchase Required Notification > edit the message > click Save Config.

Update the drop down box to say Disable to make it so anyone with a My Account on your store can send referrals. 

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