My App is supported Today Extension,
I want to add a button to my app\'s settings view, so when the user clicks on it I switch the user to \"Add Widget\"
This is not possible. The only thing you can do is to tell your users about the widget and possibly how they can add a widget to the today view:
It seems there is no API to display Widgets Edit Screen, because: Normally there is an "Add Widget" button in app's setting view by default (if widget is not installed yet). So you don't need to open widgets edit screen. Here is screenshot.
Just swipe down to open notification center and add your widget as shown in below sample.