Investigators say the caller has been using the name Aaron Foster and identifying himself as an employee of the New Castle County Courthouse.
He tells the person who answers an arrest warrant has been issued for him or her for failing to report for jury duty, and the victim must pay $100 over the phone to avoid arrest.
Several people have been targeted.
Police say no court representative would ever call asking for money over the phone and are reminding residents never to give out personal or financial information to anyone who calls.
Anyone who has been targeted by this or a similar scam is asked to call New Castle County Police at 302-573-2800.