Recently (August 2016, Google Drive app version 2.4.311.34.34 on my 2013 Moto X running Android 5.1), there is now an "Add homescreen shortcuts to your favorite files" feature. Press the three dots menu to the right of a document (in my example, "Facebook fodder"):
then scroll up until you see an "Add To home screen" item. That will put a link to your document on your current home screen.
(FYI, the first time I tried this, Google Drive failed to open the document. I killed the Google Drive app, tried again, and successfully opened the document. I have no idea how common this problem might be.)
Edit: Adding Home screen screenshot