A quick and dirty solution I have used is to place the EditText inside of a FrameLayout. The margins of the EditText control the thickness of the border and the border color is determined by the background color of the FrameLayout.
Example:
<FrameLayout
android:id="@+id/frameLayout"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:background="#000000">
<EditText
android:id="@+id/editText"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_margin="3dp"
android:background="@android:color/white"
android:ems="10"
android:inputType="text"
android:textSize="24sp" />
</FrameLayout>
But I would recommend, and the vast majority of the time I do, drawables for borders. Elite's answer is what I would go for in that case.