I ran into this issue also, assuming you already have an ActionBarDrawerToggle as @Kernald suggested, you need to add the following also to your Activity:
@Override
public boolean onOptionsItemSelected(MenuItem item) {
// Pass the event to ActionBarDrawerToggle, if it returns
// true, then it has handled the app icon touch event
if (mDrawerToggle.onOptionsItemSelected(item)) {
return true;
}
// Handle your other action bar items...
return super.onOptionsItemSelected(item);
}
This let's the toggle handle the icon button press on the ActionBar, causing the Drawer to slide out.