Officers were alerted to the scam by a woman who was targeted by the criminals.
Last Friday (July 17), a Rotherham woman received a call from somebody claiming to be from the National Crime Agency (NCA). The number he'd called from appeared to be a non-emergency SYP number - 0114 219 6905.
The man requested personal information from the victim including bank details, and claimed somebody was trying to use her National Insurance number. Luckily, this victim became suspicious and refused to hand over any sensitive details.
The force's Fraud Coordination Team are warning residents to be aware that some organised criminal gangs have the capability of making it look like they're calling from a trusted number, to make themselves seem more genuine.
PC Gavin Johnson, from the Fraud Coordination Team, said: "Fraudsters working within organised criminal gangs are becoming increasingly sophisticated, and unfortunately some have the technology to make a trusted number appear on your caller display.
"A police officer, or a representative from the NCA, would never make an unsolicited call to ask you for money or sensitive personal information such as your bank details.
"If you receive a call from somebody claiming to be an NCA officer, you can verify their identity with the NCA directly, 24/7, on 0370 496 7622.
"If somebody is claiming to be a South Yorkshire Police officer, you can take their collar number and then call us back on 101 to make sure it's a genuine enquiry. Make sure you use an alternative phone, or if you don't have another phone then wait at least 30 minutes before you call so you can ensure the fraudster has cleared the line."
Anyone who thinks they have been a victim of a scam like this should report it to Action Fraud - the national fraud and cyber crime reporting centre - by calling 0300 123 2040 or visiting their website at www.actionfraud.police.uk.