When a user performs a GET on account/settings, it returns an attribute called "discoverable_by_email", which corresponds to a checkbox at https://twitter.com/settings/account with the text "Let others find me by my email address". There is a similar checkbox at https://twitter.com/devices with the text "Let others find me by my phone number", however, this value is not represented in the account/settings resource.
Admittedly, this attribute is of limited utility, but it's inconsistent to offer access to "discoverable_by_email" while omitting "discoverable_by_phone_number".
Updates
- Thank you for the feature request, unfortunately it is unlikely that we will support this.