Some mobile carriers let you receive emails as text messages using an email-to-SMS address (for example: yourphonenumber@carriername). You could use that address when signing up, and the messages will come to you as SMS instead of regular email.
There are also services like IFTTT or similar apps that can automatically forward emails to your phone as text messages.
If you share your country/carrier, someone can point you to the exact format to use.