Can the winged dragon of Ra use its effect during another players turn?
The answer is no.

The reason why is that the Winged Dragon of Ra's effect is not a quick effect. Quick effects are monster effects you can choose to activate during either player's turn. You can think of them like quickplay spells or set traps. Quick effects are usually designated by the phrase "during either player's turn", or have the text "(quick effect)" inserted after the effect description. Winged Dragon of Ra's effect to destroy monsters reads as follows: 


  You can pay 1000 LP, then target 1 monster on the field; destroy that target.


Since it lacks a phrase that marks it as a quick effect, if Ra is in your opponent's control, it can only be activated during your opponent's main phase 1 or main phase 2, and can't be activated during your turn.