Android - How do I make this alert dialog scrollable?

In that situation you can create your own layout.xml file containing a Text View under Scroll View. and set TextMessage in this Text View, Inflate this layout with your alert dialog box.

yourxmlfile.xml

<ScrollView 
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent" >

    <LinearLayout 
        android:layout_width="fill_parent"
        android:layout_height="fill_parent" >

    <TextView
        android:id="@+id/textmsg"
        android:layout_width="fill_parent"
        android:layout_height="fill_parent"
        android:text="@string/hello" />

    </LinearLayout>
</ScrollView>

In Activity Class

LayoutInflater inflater= LayoutInflater.from(this);
View view=inflater.inflate(R.layout.yourxmlfile, null);

TextView textview=(TextView)view.findViewById(R.id.textmsg);
textview.setText("Your really long message.");
AlertDialog.Builder alertDialog = new AlertDialog.Builder(this);  
alertDialog.setTitle("Title");  
//alertDialog.setMessage("Here is a really long message.");
alertDialog.setView(view);
alertDialog.setButton("OK", null);  
AlertDialog alert = alertDialog.create();
alert.show();

This solution is take from this post.

In order for a view to scrollable, it must be nested inside of a ScrollView container:

<ScrollView>
    <LinearLayout android:orientation="vertical"
            android:scrollbars="vertical"
            android:scrollbarAlwaysDrawVerticalTrack="true">
        <TextView />
        <Button />
    </LinearLayout>
</ScrollView>

Note that a ScrollView container can only have one child layout view. It is not possible, for example, to place a TextView and Button in a ScrollView without the LinearLayout.