For instance, try something like this:
<style name="Theme.MyAppTheme" parent="@style/Theme.Holo.Light">
<item name="popupMenuStyle">@style/PopupMenu.MyAppTheme</item>
</style>
And then on the style itself:
<style name="PopupMenu.MyAppTheme" parent="@style/Widget.Holo.Light.ListPopupWindow">
<item name="android:popupBackground">@drawable/popup_menu_bg_color</item>
</style>
That is the way it's done via ActionBarStyleGenerator and some old references here on the Developer Site.