public class MyActivity extends Activity implements View.OnTouchListener {

    // Angle between pivot point and initial point of contact with the button
    private float downRadians = 0;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.my_activity);

        // Links button to XML layout and intercepts touches
        Button button = (Button) findViewById(R.id.bt_hello_button);
        button.setOnTouchListener(this);
    }
}

@Override
public boolean onTouch(View view, MotionEvent event) {
    switch (event.getAction()) {
        case MotionEvent.ACTION_DOWN:
            // Angle between the point where we first touch the view and the pivot point
            downRadians = (float) Math.atan2((event.getY() - view.getPivotY()), (event.getX() - view.getPivotX()));
            break;

        case MotionEvent.ACTION_MOVE:
            // Angle between the point the finger has moved to and the pivot point
            float moveRadians = (float) Math.atan2((event.getY() - view.getPivotY()), (event.getX() - view.getPivotX()));

            // Determines the change in rotation from when we first touched the view
            float deltaRadians = moveRadians - downRadians;

            // Rotates the button by the difference in rotation (in degrees)
            float deltaDegrees = (float) (180f * deltaRadians / Math.PI);
            view.setRotation(view.getRotation() + deltaDegrees);
            break;
    }
    return false;
}