You can contact support and they'll process the deletion for you (similarly, you can contact them to have SEDE profiles merged as needed).
There's no self-serve option as noted in comments. They will ask you to verify ownership of the profile, so putting "Delete me" in the "About me" section of the profile will help them simply process the request and let you know it was completed.
If you don't have access to the OpenID associated with the account anymore (e.g. MyOpenID) let them know, and indicate the email address associated with it in your request for verification (they may ask for a few other things just to be sure).