Shaw is the first USC cornerback to be drafted since Kevin Thomas was chosen in the third round in 2010.
Shaw, 6 feet and 201 pounds, was selected despite sitting out 10 games last season after he was suspended for fabricating a story about how he suffered ankle injuries on the eve of the opener.
Shaw, 22, said he had been injured attempting to save a young relative who was in distress in a swimming pool. But he later acknowledged that he had jumped from a balcony at his apartment complex to avoid police, who had been called to investigate a possible domestic violence incident.
Shaw played the final three games for the Trojans, and then impressed talent evaluators during the East-West Shrine game and the Senior Bowl.
He ran the 40-yard dash in 4.44 seconds at the combine and bench-pressed 225 pounds 26 times.
He finished his USC career with six interceptions.