How to use the filter ‘widget_text’ to a particular text widget with id

Is it default text widget? If yes, then I don’t think there is a way.

Why don’t you create a custom text widget? And before echoing output process the text whatever you wants to do?

The logic is, you will create another widget, that will take some text (or html?) and you will process that text, add some data what you want and show as output 🙂