Yes, you can! It's not in the UI yet, but the format for the remix URL is
name is an arbitrary name that helps make the URL memorable/identifiable, and
projectId you can get by viewing the console output in developer tools - it’s outputted to the console when your project loads. You can also get it by running
application.currentProjectId() in the dev tools console. Putting those together you’ll get something like:
If you have any problems getting the projectID, then let me know the project name and I'll create the link for you.