This Widget is provided by the Jetpack Plugin.

To add it:

1. Activate the Jetpack Plugin
2. Activate Extra Sidebar Widgets in the Jetpack->settings section of the Dashboard.
3. Add the widget on the Widgets section of the Dashboard Appearance->Widgets.
4. You can add your twitter name to show a profile or an id to show a search. NB as of September 2018 twitter have changed their service again, you can no longer use the ‘Widget ID’ option.

More details on the jetpack blog:

Extra Sidebar Widgets – Twitter Timeline