You cant because it is a predefined widget.
You can work around it with a Row widget:
Scaffold(key:_scaffoldKey,drawer: Drawer(),appBar: AppBar( automaticallyImplyLeading: false title: Row( mainAxisAlignment: MainAxisAlignment.start, crossAxisAlignment: CrossAxisAlignment.center, children: <Widget>[ SizedBox( height: 20, // Your Height width: 20, // Your width child: IconButton( // Your drawer Icon onPressed: () => _scaffoldKey.currentState.openDrawer()), icon: Icon(Icons.arrow_back, color: Colors.white), ),) // Your widgets here ], ), ),)
You need the Key to open the drawer with _scaffoldKey.currentState.openDrawer().
automaticallyImplyLeading: false will prevent the default drawer Icon.