Yes, it is possible.
However, before you begin, please make sure you have followed the instructions on How to set up a domain for short links.
To add www to your domain
Go to your domain registrar and add a CNAME record as follows:
Host: www
Type: CNAME
Value: cname.short.io
Important notes:
If the domain is Inactive in Short.io, then wait for a few hours and click on Refresh to check if the status has changed
In order to reissue your SSL certificate (to include the www version as well), please contact the Short.io support team
Hereafter, the links you shorten using this domain can be accessed in one of two ways: either with or without www at the beginning.