Is it possible to change the radio button icon in an android radio button group

Yes that’s possible you have to define your own style for radio buttons, at res/values/styles.xml:

<?xml version="1.0" encoding="utf-8"?>
<resources>
<style name="CustomTheme" parent="android:Theme">
   <item name="android:radioButtonStyle">@style/RadioButton</item>
</style>
<style name="RadioButton" parent="@android:style/Widget.CompoundButton.RadioButton">
   <item name="android:button">@drawable/radio</item>
</style>
</resources>

‘radio’ here should be a stateful drawable, radio.xml:

    <?xml version="1.0" encoding="utf-8"?>
    <selector xmlns:android="http://schemas.android.com/apk/res/android">
    <item android:state_checked="true" android:state_window_focused="false"
        android:drawable="@drawable/radio_hover" />
    <item android:state_checked="false" android:state_window_focused="false"
        android:drawable="@drawable/radio_normal" />
    <item android:state_checked="true" android:state_pressed="true"
        android:drawable="@drawable/radio_active" />
    <item android:state_checked="false" android:state_pressed="true"
        android:drawable="@drawable/radio_active" />
    <item android:state_checked="true" android:state_focused="true"
        android:drawable="@drawable/radio_hover" />
    <item android:state_checked="false" android:state_focused="true"
        android:drawable="@drawable/radio_normal_off" />
    <item android:state_checked="false" android:drawable="@drawable/radio_normal" />
    <item android:state_checked="true" android:drawable="@drawable/radio_hover" />
    </selector>

Then just apply the Custom theme either to whole app or to activities of your choice.

For more info about themes and styles look at http://brainflush.wordpress.com/2009/03/15/understanding-android-themes-and-styles/ that is good guide.