Delicious API – Is Delicious Feeds API No Longer Supported?

You can't, but you can create a new account and import your exported bookmarks from your old account.

From the Delicious FAQ:

How do I change my username?
There's no easy way to do this right now, but you can use the export and import features in your settings to change to a new account while preserving your current bookmarks. First, visit your Settings (accessible from the top right of every page on Delicious) and select export/backup from that page. Follow the directions to export your bookmarks. Then, register or log into your new account, go to settings, and select import/upload. After importing your bookmarks into your new account, you can log out of it and log back into your old account to delete that one. To do this, go to Settings and choose delete account.

Importing all Delicious bookmarks seems to work now.

Go directly to the import page or log in, then go to My Account -> Tools -> Import bookmarks from Delicious