No, the Dark Lord didn’t know a piece of his soul was in Harry.
When Dumbledore explains to Harry what happened when they meet in King’s Cross, he tells Harry that the Dark Lord didn’t know he’d left part of his soul behind along with his body.
“You were the seventh Horcrux, Harry, the Horcrux he never meant to make. He had rendered his soul so unstable that it broke apart when he committed those acts of unspeakable evil, the murder of your parents, the attempted killing of a child. But what escaped from that room was even less than he knew. He left more than his body behind. He left part of himself latched to you, the would-be victim who had survived.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Additionally, the Dark Lord doesn’t feel when the Horcruxes are destroyed, so it’s unlikely that he’d feel that another piece of his soul was missing from the main part.
“Does Voldemort know when a Horcrux is destroyed, sir? Can he feel it?’ Harry asked, ignoring the portraits.
‘A very interesting question, Harry. I believe not. I believe that Voldemort is now so immersed in evil, and these crucial parts of himself have been detached for so long, he does not feel as we do.”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
Despite that, up until the day before the Dark Lord’s death when he discovered that most of his Horcruxes were destroyed, the Dark Lord believed he would feel it if anything happened to his soul.
“But surely if the boy had destroyed any of his Horcruxes, he, Lord Voldemort, would have known, would have felt it? He, the greatest wizard of them all, he, the most powerful, he, the killer of Dumbledore and of how many other worthless, nameless men: how could Lord Voldemort not have known, if he, himself, most important and precious, had been attacked, mutilated?”
- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)
Because of this, it seems unlikely that the Dark Lord ever figured out that a piece of his soul was in Harry, since he’d presume he’d know where all the pieces of his soul were.