I had a teacher come to me this morning who is really tired of the plethora of emails that she gets from students sharing their assignments with her. There are many solutions to it, but I thought that this might be the easiest way. The basic premise is that you are going to create a Google Form for your students to fill out that contains a link to their assignment that they are "passing" in. If you set up your form to record their user name, then all you really need is the link, but you can also include a drop down menu of what the assignment is.
Fortunately, the Florida Institute of Technology has a handy step by step document that walks you through how to do it on your end and how your students fill it out. You can then embed the form on your website to make it even easier for your students to use it and increase traffic to your own page.
For advanced users, I would go so far as to use Form Ranger to automatically populate a drop down question type with a list of the assignments they can chose from to submit. But that's certainly a bit more work than a simple Google Form and you can meet with me if you are interested in making it happen.