Check out the FAQ to add a verified outgoing caller id.
To use the REST API, POST your phone number to the Outgoing Caller IDs list resource.
Here's an example to add a new Outgoing Caller ID in PHP:
<?php
// Get the PHP helper library from twilio.com/docs/php/install
require_once('/path/to/twilio-php/Services/Twilio.php'); // Loads the library
// Your Account Sid and Auth Token from twilio.com/user/account
$sid = "ACXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";
$token = "your_auth_token";
$client = new Services_Twilio($sid, $token);
$caller_id = $client->account->outgoing_caller_ids->create("+14158675309", array(
"FriendlyName" => "My Home Phone Number"
));
echo $caller_id->validation_code;