The Australian batsman was drafted in by the Rapids as a replacement for compatriot Travis Head after his earlier than expected call-up into the ODI squad to face England.
Ferguson responded by smashing his runs from just 143 balls with five sixes and 21 fours as the table-topping Rapids overhauled Leicestershire's imposing 4-376 with 16 deliveries to spare.
It was Worcestershire's highest individual List A score, beating fellow Australian Tom Moody's 180 against Surrey in the 1994 NatWest Trophy semi-final at The Oval.
Callum Ferguson is third Worcestershire player to score a century on List A debut for the county after Phil Jaques (2006) and Phil Hughes (2012)— Worcestershire CCC (@WorcsCCC) May 29, 2018
Ferguson produced an awesome display of hitting but received excellent support from Joe Clarke, Daryl Mitchell and Brett D'Oliveira in securing a fourth win in five matches in the competition for the Rapids.
There were just seven needed when he was caught behind off Varun Aaron and he left the ground to handshakes from many of the Leicestershire players and a standing ovation.
The Rapids' total was their highest ever in 50-over cricket against first-class opposition, surpassing the 361 for eight made against the Foxes in the same competition last summer at the Fischer County Ground.
Leicestershire's own total was their highest in List A cricket against a first-class county, overhauling their 363 for seven in 2017 against Warwickshire.
But Ferguson and his teammates made mincemeat of their target as they took another big step towards securing a place in the knockout stages.
"I was just really grateful to get the opportunity to play here. To play domestic cricket over here was something I was really excited to get the chance to do," Ferguson said.
"To be able to get off on the right foot and make some runs is really exciting. It is certainly better than nought on debut.
"I had a few nerves coming into the game and was really pleased to be able to make an impact and hopefully we can keep the ball rolling in the next few games."
Ferguson's SA captain Head has scored 291 runs and two half-centuries from five Division One matches with Worcestershire.
He also top-scored for the Rapids with 77 in their four-run one-day victory over his former county club Yorkshire last Wednesday.
Fellow Redbacks fast bowler Joe Mennie has 16 wickets at 21 with best figures of 3-4. He claimed 3-56, including the wicket of Head, in his last one-day outing for Lancashire.