The offence is reported to have happened on Friday at a house in the Lidget Green area of the city.
At around 7pm, the culprit knocked on the door and offered to remove some rubbish from the garden for a small payment. The occupant, a man in his fifties, agreed and handed over some cash.
The child, who was believed to be a girl of around five-years-old, then asked for a drink and went into the house to make one.
The occupant later found that around £40 had been taken from his wallet.
Police said that the alleged offender is described as a white male of stocky build and around 5ft 8ins tall.
He had short brown hair, was wearing a high visibility jacket and spoke with what the occupant believed was an Irish accent.
Detective Inspector Warren Pitman, of Bradford District Police, said: “While this appears to be an isolated incident, it is a commonly known way for criminals to steal from your property.
“We would advise people not to accept offers of work from doorstep callers and to report this kind of activity to the police.
“We would also advise people to keep their doors and windows locked when they are at home and not to open doors fully when speaking with unexpected callers.
“Callers who appear to be workmen should carry some form of identity, so always ask to see this before letting anyone into your property. If you’re still unsure ask for a number to call so you can check. Genuine callers will not mind waiting.
“If you’re still unsure keep your doors locked and contact the police on 101, giving as much information as you can about the caller and any vehicle they appear to be using.”
Anyone with information about the offence in Lidget Green is asked to contact police on 101, quoting crime reference 13180002703.