I don't know it's a bug from Twitter or they want it lol. In my side, I have tried time to time to input my mobile phone to my account and the result is
WTF! Why VietNam is still not support? Gru Gru
For anyone who angry like me can use these steps:
1. Download twitter application to your iPhone.
2. Go to Account tab > Settings > Choose "your name"
3. Go to Security tab
And awesome! I can input my mobile phone without carier and can receive verification code as well.