Well, at WWDC Apple introduced iOS 6 with all the features included. One of which is the advancement in social sharing, like you can share to Twitter form Notification Center.
Albeit Twitter Widget is not a new thing in jailbreak realm, but since the Apple showed his own with all the aesthetics and design, has provoked an iOS developer to juggle his own version that almost similar with what Apple's offer.
And now we are going to grab a tweak from Cydia in order to achieve that. The tweak's name is iOS 6 Twitter Widget for Notification Center, currently stored under BigBoss repository and it's free! Supports iOS 5 or newer.