You can create a focus listener on the EditText on the AlertDialog, then get the AlertDialog‘s Window. From there you can make the soft keyboard show by calling setSoftInputMode.
final AlertDialog dialog = ...;
editText.setOnFocusChangeListener(new View.OnFocusChangeListener() {
@Override
public void onFocusChange(View v, boolean hasFocus) {
if (hasFocus) {
dialog.getWindow().setSoftInputMode(WindowManager.LayoutParams.SOFT_INPUT_STATE_ALWAYS_VISIBLE);
}
}
});