The Independent Police Complaints Commission (IPCC) said it was looking into more than 100 allegations.
It said complaints had been made against 42 named officers and a number of "unknown" officers.
The complaints include allegations of neglect of duty and of corruption.
In a statement the IPCC said its investigation had "expanded" since it announced in November it was investigating 10 officers involved in incidents highlighted in Professor Alexis Jay's report into child sexual exploitation (CSE) in Rotherham.
The Jay Report, published in August, found the abuse of 1,400 children in the town over a 16-year period was ignored by agencies.
The IPCC said: "Since that announcement we have received 30 complaints relating to South Yorkshire Police's handling of CSE in Rotherham.
"The complaints contain more than 100 allegations against 42 named police officers, both retired and serving, as well as a number of allegations against officers whose identities are currently unknown.
"Work to establish the identity of the unknown officers and to identify any links between the different complaints and incidents is ongoing.
"The allegations range from neglect of duty by failing to adequately investigate on the basis of intelligence or to deal with incidents appropriately, inappropriate comments and suggestions of corrupt relationships between police officers and offenders."
It said it was also investigating a claim that South Yorkshire Police "failed to act on information passed to them in 2004 and 2006 about alleged child sexual exploitation in Sheffield", in relation to two named officers who are now retired.
In a statement, the force said: "South Yorkshire Police has referred a number of allegations to the Independent Police Complaints Commission (IPCC) in relation to child sexual exploitation in Rotherham.
"We remain committed to assisting them with their independent investigation into any alleged misconduct."

Set in a grand retirement home for ageing musicians, Quartet marks the 75-year-old's debut as a film director.
The film has its gala screening at the London Film Festival on Monday night.
Based on Ronald Harwood's play, Quartet is set in a home for retired musicians, where old rivalries are stirred up by the arrival of former opera singer Jean Horton (Dame Maggie Smith).
She is joined in the cast by British heavyweights Tom Courtenay, Billy Connolly,  Pauline Collins and Michael Gambon.
But Hoffman, who says the the story is about people in their "third act", hired a supporting cast of real-life elderly performers to give his film authenticity.
"For these people the phone hadn't rung for 20, 30 or 40 years, even through they can deliver," he said on Monday.
"These people in their 70s, 80s and 90s came with such verve every day - and that in itself made this an extraordinarily special occasion for all of us."
Released in the UK in the new year, the film follows the box office success of The Best Exotic Marigold Hotel, another ensemble piece about a group of British pensioners in a retirement hotel in India.
"I think a lot of grown-ups would like films for grown-ups and about grown-ups," said Dame Maggie, who also starred in Marigold Hotel.
"I don't think films about elderly people have been made very much, but they always seem to be fairly successful."
The youngest member of the principal cast is Sheridan Smith, who plays the retirement home's medic, Dr Lucy Cogan.
The actress said it had been "overwhelming" to be part of the film.  "I tried to be like a sponge and take it all in."
Hoffman's movie breakthrough was as Benjamin Braddock in 1967's The Graduate, for which he was Oscar nominated. He has also had nominations for Midnight Cowboy, Lenny, Tootsie and Wag the Dog.
He won the Oscar in 1979 for his role in Kramer vs Kramer and again in 1988 for Rain Man.
Asked about Hoffman's skills as a debut director, Pauline Collins said: "Dustin is a dynamo and a darling. He's one of the most inspiring and kindest directors I've ever worked for because he understands how actors work because he is one."
Explaining why it hadn't taken him so long to step behind the camera, Hoffman said: "Sometimes it takes you 40 years to get around to doing something."
The police watchdog has said it is investigating complaints against 42 South Yorkshire Police officers over the handling of child sexual exploitation in Rotherham.
[NEXT_CONCEPT]
Dustin Hoffman has sung the praises of the retired opera singers and musicians who appear in his new film, Quartet.