How can I implement OnPressed callback for Text widget, Flutter

Use InkWell

this gives you nice ripple effect as well

 new InkWell(
          onTap: () {
            Navigator.pushNamed(context, "YourRoute");
          },
          child: new Padding(
            padding: new EdgeInsets.all(10.0),
            child: new Text("Tap Here"),
          ),
        );

or

new FlatButton(
          onPressed: () {
            Navigator.pushNamed(context, "YourRoute");
          },
          child: new Text("Tap Here"),
        )

Just wrap your title in a GestureDetector to handle clicks. Then call Navigator's pushNamed to redirect to a new route.

new GestureDetector(
  onTap: () {
    Navigator.pushNamed(context, "myRoute");
  },
  child: new Text("my Title"),
);