Yes, it would be possible. I don't think there's an easy (plugin) solution for this purpose, though. If your project has an active module, you could use that to save the click count and retrieve it from the DB.
- Make sure your module works (in the default Craft project, it's as simple as uncommenting the module line in
- Create a migration to create a table in which you store the click counts (per url, or by ID if each link has a unique ID)
- Create a model to interact with your table
- Create a controller method to handle the clicks (get DB row for URL, add 1, save it)
- Create a template variable to get the click count for a URL
After that, all that's left is writing some JS to listen for link clicks and POST the URL to your controller method.
All in all, not very easy if you're new to PHP (be sure to read this before you start), but a nice first dive into Craft plugin/module development.