Creating an Email Referral Program

I am a marketing coordinator for Broward College Student Life and we just recently started an email marketing campaign that highlights upcoming events and programs for students. We want to grow our audience of subscribers for the emails and I recently came across Morning Brew, which does a referral program where the subscriber receives a custom referral link that can be shared with friends and at benchmark referral amounts (5, 10, etc) that person gets a gift. I am interested in creating a system like this that generates a link to be shared and tracks how many people used that link. If someone would be willing to guide me through the process or lead me in the right direction I would much appreciate that! Thank you so much for your time and consideration.