if neither the king or the rook has moved by that point in the game it is legal to castle in that position. But I would just take the knight :)
Castling Question
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Black cannot castle because the caption says white to move, and black cannot castle on white's turn. If it were black's turn then he could legally castle, although it would be better to take the knight.
To castle the king may not be in check or pass through check. How about this position? Can Black castle?