The first call that came through to the service was a report of a car parked across someone's driveway.
As of Monday, 53,000 calls had been taken by 105 operators.
A police spokeswoman said the number was being "widely used" for a variety of non-emergency situations including thefts from public places and cars, intentional damage to property, shoplifting and lost property.
Of the calls being made, 14 per cent relate to matters previously reported to police.
A further 21 per cent are from people seeking advice from police.
"Since we've launched the marketing campaign and the 105 jingle, we're seeing daily increases in the number of people calling 105 to report non-emergencies, rather than other channels," the spokeswoman said.