You can upload your app to github, connect zenodo (https://zenodo.org/), make a release on GtiHub and get DOI from zenodo. Then reference to your app is DOI, that could be merged with some "Availible on-line bla-bla-bla.shinyapps.io".
If you are interested in writing a paper about your app --- it will be the same. Write a separate paper describing something with DOI you abtained previously.