Officers in New Jersey are planting dummy boxes fitted with GPS trackers, coupled with hidden doorbell cameras, at homes around the city of Jersey.
The homes selected for the experiment were chosen using the city's own crime statistics combined with mapping data of theft locations supplied by Amazon.
One box was stolen three minutes after it was "delivered".
Amazon told AP: "We appreciate the increased effort by local law enforcement to tackle package theft and remain committed to assisting however we can."
The US Postal Service expects to deliver about 900 million packages in the run-up to Christmas.
Last year, Amazon launched a service called Amazon Key that allowed homeowners with smart locks to let couriers open their doors via an app and leave parcels inside.
While that may be a step too far for many, there are other ways to protect deliveries:
Have them delivered to a workplace or a friend who is home during the day
Insist that deliveries must be signed for
Install cameras that will give police some video evidence
Use a service that provides a storage box drivers can unlock by entering a code on a keypad
Amazon also provides lockers for people to pick up parcels in locations such as shopping centres, convenience stores, airports, train stations and universities.
Source: BBC