How to add theme to Android ActionMenu

I am following this S.O. post about changing the appearance of the Action overflow menu, and it tells me to create a theme to create the desired changes.

I know how to create a theme, and I know how to apply a theme to the whole application or a specific activity, but I don't understand how to apply a theme specifically to the ActionBar / Action Overflow Menu.

From the accepted answer of the above mentioned S.O. post, I've created this theme. Could someone help me understand how to apply it to the ActionBar / Action Overflow menu?

<style name="OverflowMenu" parent="Widget.AppCompat.PopupMenu.Overflow" >
    <item name="overlapAnchor">false</item>
    <item name="dropDownVerticalOffset">?attr/actionBarSize</item>
</style>