In the Admin Module, expand Settings and click on Custom Fields. There should be a client field named Referred By. If not you can create a new client field and name it anything you want to. Choose the type of Textbox or Drop Down List. Enter the remaining information and click 'Save'.
Then, expand Online Registration on the left admin menu and click on Registration Forms. Create a new Client Form. Give the new form a name and choose the field from the above step. You can also make it required. Then click 'Save'.
Now you can assign that form so that every time a new client registers in the system they will be able to fill out that form. Expand Online Registration on the left admin menu and click on Configuration. In the Client Settings section choose the new form you created above and click 'Update'.
Now every time a new client registers they will see that form and your referral field. You can then view the entered value under the 'Fields' tab on the client's page.