Is there a way to turn a web page into an app-like link on the android home page?
Bookmark the page in Chrome for Android. Go to your bookmarks, long-press on the bookmark, and click "Add to Home Screen".

Source:
http://howto.cnet.com/8301-11310_39-57416489-285/how-to-add-chrome-for-android-bookmarks-to-your-home-screen/

Works on my Galaxy S4 and Nexus 7.