D'Acquisto was drafted by the San Francisco Giants in the 1st round of the 1970 MLB Draft out of St. Augustine High School in San Diego, California. He made his Major League debut on September 2, 1973 against the Atlanta Braves, starting the second game of a doubleheader. He allowed 2 runs in 4.2 innings and did not get a decision. He pitched a complete game victory over the San Diego Padres on September 21 for his first career win while striking out 11. Overall, he was 1–1 with a 3.58 ERA in 7 appearances that year. D'Acquisto was named National League Rookie Pitcher of the Year in 1974 when he went 12–14 with a 3.77 ERA for the fifth-place Giants, but he missed most of the next season after elbow surgery. He tied an NL record with three wild pitches in one inning on September 24, 1976. In 4 seasons with the Giants he was 18–27 with a 4.68 ERA in 83 appearances.
St. Louis Cardinals
He was traded to the St. Louis Cardinals for Willie Crawford, John Curtis and Vic Harris on October 20, 1976. Due to his being on the disabled list, D'Acquisto only appeared in 3 games with the Cardinals with a 4.32 ERA.
San Diego Padres
The Cardinals traded him to the San Diego Padres on May 17, 1977 for Butch Metzger. In 1978 he was switched to the bullpen. In 1979, D'Acquisto was put back into the rotation and had 51 appearances with a 9–13 record with 134 innings pitched and struck out 97 batters. In 4 seasons with the Padres he was 16–21 with a 4.24 ERA in 152 games.
On August 11, 1980 he was traded to the Montreal Expos for a player to be named later. He made 11 appearances out of the bullpen with the Expos, with a 2.18 ERA.
In 1981 D'Acquisto tested the free agent market and signed with the California Angels. D'Acquisto did not pitch much with the Angels during the strike-ridden year and was subsequently sent to the minor leagues in Salt Lake City, Utah. He was brought back to the parent team in spring training and then released.
Atlanta Braves
After his release, he signed with the Atlanta Braves and was sent to Richmond AAA International League in 1982. He asked for, and was granted, his release on July 27, 1982.
He signed with the Oakland Athletics under Billy Martin and pitched for Oakland for the rest of the 1982 season. D'Acquisto was part of the A's in spring training the next year also but was released on the last day of spring training.
After he retired from baseball, D'Acquisto became a registered investment advisor. In 1996, D'Acquisto was sentenced to five years and three months in prison for trying to pass off a forged $200 million certificate of deposit. D'Acquisto was also indicted in 1998 on charges of defrauding investors of approximately $7 million. As a result, D'Acquisto was sentenced the following year to an additional four years and seven months in prison after he pleaded guilty to wire fraud and money laundering.