How can I post to Twitter using Siri?
Workaround
Because Twitter offers to update your status via SMS, there is an easy workaround.

Create new Contact
Assign as first name: Twitter
Assign phone number:  40404   (this number is for United States residents)

Now you can update your Twitter status via Siri:

Tell Twitter Hello World.

Enable SMS for Twitter
In order for the workaround to work, you need to enable the SMS feature for Twitter first.
You can do this either online by editing your profile on twitter.com or send the text message start to 40404 (for US residents only!). Then follow the instructions in the reply. However, the latter way is more complicated.
International Twitter SMS codes
United States    40404
United Kingdom   86444        (Vodafone, Orange, 3 and O2 customers)
Australia        0198-089488  (Telstra customers)
...

You can get a full list of the world-wide twitter short codes here.
Some countries or providers do not support short codes. You have to use long codes instead. Fees may apply:
United Kingdom  +44-762-4800379
Germany         +49-157-05000021
Finland         +35-845-73950042