When publishing a promotion to Twitter you can customize your header banner so a pre-populated tweet appears when they click on the banner. To do this, upload an image that you want to appear, such as an image with text saying "Tweet your Entry"

For the click through URL type in http://twitter.com/home?status=%20

followed by the tweet you want to pre-populate, separating each word by %20, you should also include a bit.ly to link back to your campaign. 

Here is where the banner will populate:

When they click through, the tweet will automatically come up: