The tweet widget “tap to tweet” in the notification center is gone in iOS 7. But you can still tweet from the notification center by using MyShortcuts+Viewer.
Here are the links for installing a tweet item. Choose your twitter client and tap one of the links below after you installed MyShortcuts app onto your iPhone/iPod touch/iPad. The reminder screen will come up. Just save as is. Then the tweet item will show up in the notification center as a notification.
Official Twitter Client
Now, you can tap and tweet by tapping the tweet item in the notification center.