Only old Dropbox accounts also can share their folders for free - so there is no way with a newer one.
But Dropbox isn't the only cloud storage solution.
As far as I know you could use the Microsoft Onedrive (works for me) - here it is possible to share folders even with a free account.
You could also use other services - there are plenty to choose from.
If you want to share your game - so it could get played - you should think about a free webspace (without commercials), where you upload your game via FTP.
I think https://www.bitballoon.com/ will work (please let me know)