Board Thread:Questions and Answers/@comment-9826910-20130618064245/@comment-11477779-20130809042724

Sternritter M wrote:

Regarding SS figuring out Ichigo's heritage:

Byakuya could have enough knowledge/experience about human aging to guess Ichigo's age. He saw that Ichigo strongly resembled Kaien, and he knew that Kaien was a Shiba. He could have considered that and put Ichigo's age in comparison to the 20 years that had passed since Isshin disappeared. Furthermore, Byakuya must have considered the possibility of Ichigo being part Shinigami because of the great Shinigami powers he had at such a young age.

So, he could have come to the conclusion that Isshin must have settled in the human world and eventually become the father of Ichigo.

If he did figure it out it was long after the Rescue arc. While they were fighting on Sôkyoku hill and Byakuya was talking to himself he couldn't understand why Ichigo had these abilities because "he's not a noble" which is untrue if he knew his roots and still thought the source of his power was from Rukia. At that point Byakuya had no clue who Ichigo really was.