Yes! Full rules including castling (kingside and queenside), en passant, pawn promotion with piece selection, check, checkmate, and stalemate detection.
When your pawn reaches the opposite end of the board, you'll be prompted to choose a piece: Queen, Rook, Bishop, or Knight.
Click your King, then click the square two spaces to the left or right. Castling is only available if neither the King nor the Rook has moved, and no squares between them are under attack.