Add campaign tracking codes to the links in your app.
E.g. if you use the "cid" parameter for your campaign tracking code in AA, then in your app's link, e.g.
https://www.website.com/link-from-app-to-website
Add the "cid" parameter with an appropriate tracking code, e.g.
https://www.website.com/link-from-app-to-website?cid=app-link
In your website's AA, you can run a report with Tracking Code and find all instances of that "cid" parameter's value. The number will be the number of "taps" from your app to your website.