var rendererOptions = {
draggable: true
};
This is the code snippet which I tested for my university project on how to drag the current route of Google maps. As you guys can see Google maps it self providing this feature hence I was curious how to do it.. Finally I found this pretty simple code snippet. Add this in the <head> section of your particular web page.
And then this simple code
var directionsDisplay = new google.maps.DirectionsRenderer(rendererOptions);
then add this variable to where you are declaring the map
directionsDisplay.setMap(map);