Can I use the effect of the Winged Dragon of Ra from the Yu-Gi-Oh! anime in a real game?
Effects from the Yu-Gi-Oh! anime do not apply to the card game, especially not in a legal tournament. You can only use the text that is actually on the card (and any modifications due to errata or official rulings).

Of course, in a friendly game, you and your opponent are welcome use those affects if you agree. If you want to play that way, nothing is stopping you.