First, go to this website for I-card information: http://www.byui.edu/financial-services/my-account/i-card. There is a link there for online degree students to fill out.
Here is the link for the direct for online degree students to fill out an application for an I-Card: http://www.byui.edu/financial-services/my-account/i-card/online-student-i-card-application-form.