Вы можете использовать ActionBarDrawerToggle
final DrawerLayout drawer = (DrawerLayout) findViewById(R.id.drawer_layout);
ActionBarDrawerToggle toggle = new ActionBarDrawerToggle( this, drawer, toolbar,
R.string.navigation_drawer_open, R.string.navigation_drawer_close);
toggle.setDrawerIndicatorEnabled(false);
toggle.setHomeAsUpIndicator(R.drawable.myicon);//your preferred drawable image here
toggle.setToolbarNavigationClickListener(new View.OnClickListener() {
@Override
public void onClick(View view) {
drawer.openDrawer(GravityCompat.START);
}
});