How to have a custom URL for an icon on the iOS home screen

Is it possible to make a custom URL for an icon on the iOS home screen? Or at least have a way for the user to edit the URL themselves?

UPDATE: To be more specific, here's what the client said:

"Because of our use of authentication, the URL of the landing page that [website] takes you to changes to a long URL with a session ID. Right now, when I use the Add to Home Screen function, it associates the icon with the long URL which, because of the session ID, won't work after a couple of days. Is there any way to change the URL to [website] (our stable and persistent URL) after or before the Add to home screen function is invoked"

Also, the website isn't a web app, so I'm not sure if web app things would apply here.....?

Solution

This answer is no longer valid.

No, it's not possible to do this because of security constraints. You need to handle those expired session IDs on the web application side - it's usually done with a redirect to the authentication page, most web frameworks should do this out of the box for you.