To resolve this error, follow these steps:
(Note: The images below are from the Mac version of the Safari browser, but the same process applies using an iOS browser.)
1. Go to dayone.me/user/login, then click *Authenticate with Apple ID*.
2. Sign in using your Apple ID email address and password. (Note: This uses an official Apple-provided-and-secured web service.)
3. Click *Account*, then click *Delete Account*.
4. To confirm this choice, click the *Authenticate with Apple ID* then sign in again.
5. Click *Delete My Day One Account*.
6. Go to dayone.me, and sign in using your original Day One account email address and password.
7. Click *Account*, then click *Link Apple ID*.
8. Sign in using your Apple ID email address and password.
After completing the above steps, your Apple ID is now linked with your account.