It was designed to be like that! See ...
http://www.bbc.co.uk/news/special/2014/newsspec_7141/index.html
Da Silva Costa, whose design was chosen in February 1922, imagined the statue facing the rising sun: “The statue of the divine saviour shall be the first image to emerge from the obscurity in which the earth is plunged and to receive the salute of the star of the day which, after surrounding it with its radiant luminosity, shall build at sunset around its head a halo fit for the Man-God,” he wrote.
The whole article is an interesting read ...