Swimming is allowed in the Bosphorus, but as a protip DO NOT SWIM IN IT. The water is highly traversed by massive ships each day and is extraordinarily polluted. Not only that, but the currents and riptides in the strait are quite dangerous and there are no life guards. If you have an unquenchable yen for swimming in the Bosphorus, I'd recommend the Annual Bosphorus Swim, a cross continental race held each year in July. The race has lifeguards and a reputation as super difficult, so start training now.