다음과 같이 하시면 될 것 같네요.
	1. Picker를 startActivityForResult()로 호출
private void showRingtonePickerDialog() {
	Intent intent = new Intent(RingtoneManager.ACTION_RINGTONE_PICKER);
	intent.putExtra(RingtoneManager.EXTRA_RINGTONE_TITLE, "Select ringtone for notifications:");
	intent.putExtra(RingtoneManager.EXTRA_RINGTONE_SHOW_SILENT, false);
	intent.putExtra(RingtoneManager.EXTRA_RINGTONE_SHOW_DEFAULT, true);
	intent.putExtra(RingtoneManager.EXTRA_RINGTONE_TYPE,RingtoneManager.TYPE_NOTIFICATION);
	startActivityForResult(intent, 777);
}
	2. onActivityResult() 콜백 함수에서 Uri 읽음.
@Override
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
	super.onActivityResult(requestCode, resultCode, data);
	if (resultCode == RESULT_OK) {
		switch (requestCode) {
		   case 999:
					Uri uri = data.getParcelableExtra(RingtoneManager.EXTRA_RINGTONE_PICKED_URI);
					if (uri != null) {
						String ringtonePath = uri.toString();
						Toast.makeText(getApplicationContext(), "ringtone="+ringtonePath, Toast.LENGTH_LONG).show();
					}
		   break;
		default:
		   break;
		}
	}
}