One simple way is to wrap your Spinner + Drop Down Arrow Image inside a Layout. Set the background of Spinner as transparent so that the default arrow icon gets hidden. Something like this:
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:background="@drawable/background"
android:orientation="horizontal">
<Spinner
android:id="@+id/spinner"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_gravity="center"
android:layout_weight="4"
android:gravity="center"
android:background="@android:color/transparent"
android:spinnerMode="dropdown" />
<ImageView
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center"
android:layout_weight="1"
android:onClick="showDropDown"
android:src="@drawable/ic_chevron_down_blue" />
</LinearLayout>
Here background.xml is a drawable to produce a box type background.
<shape xmlns:android="http://schemas.android.com/apk/res/android">
<solid android:color="@android:color/transparent" />
<corners android:radius="2dp" />
<stroke
android:width="1dp"
android:color="#BDBDBD" />
</shape>
The above code produces this type of a Spinner and icon.
