Add-on to Advanced custom fields giving you a field to display Widget Areas.
For this plugin to work, you need to have the Advanced Custom Fields Plugin installed. Once installed, you will be able to select a Widget Area as one of your custom fields.
The WordPress Codex has an article on Widgetizing Themes which includes "How to Register a Widget Area". If you add a new Widget Area (also called sidebar) with this method it will be available in Appearance > Widgets and also able to be selected in your new Widget Area Field.
The Advanced Custom Fields website has documentation on displaying custom field values.