Automatically log someone into a Wordpress site from an app

So I have a website that sells digital downloads. For the past couple of months I have built a desktop OS X Application in Xcode Swift 3. I have successfully handled logging in using my Wordpress database of users. I simple check if the user exists and create a global variable to use "isLoggedIn". I also have handled payment processing and I am using links from the website to supply the user with a link that starts the download of their purchase. When the user clicks the link it prompts them to log into the site even though they are already logged into the application. Is there a way to automatically log a user into the Wordpress site based on the credentials they already entered in the app so that they can access the digital download link? Unfortunately these links must go through the site because they run extra security when being downloaded that is required.