The most direct equivalent of the iOS Activity Indicator in Android is the ProgressBar but set to indeterminate. So you can drop the view into your layout and it will provide you with a spinning animation.
<ProgressBar
android:layout_height="wrap_content"
android:layout_width="wrap_content"
android:id="@+id/ctrlActivityIndicator"
android:indeterminateOnly="true"
android:keepScreenOn="true"
/>
You could use this to indicate some background activity to the user.