This is now easier with the coming iOS 9, because cookies can be shared between Safari and the in-app Safari View Controller! Simply keep a cookie in the browser and track the last link clicked on. Then when the user opens your app, open up an invisible Safari View Controller in the background while you show a spinner. As soon as you can inspect the cookie and see the last link clicked, you can stop the spinner–it should be a very fast operation.
We offer this for no cost at Branch, where we’ve had a customizable web banner for some time. Now we’re excited to incorporate the Safari View Controller into our open-source SDK! We also have a version of digital fingerprinting that allows you to do the same on pre-iOS 9 devices. We use IP address, OS, OS version and more to compare a click in a browser to an open in an app. This approach has pros and cons.. happy to go into further detail if you’re interested.