Defabricator

The defabricator was a device from the year 200,100. It was previously used by the Trin-e and Zu-Zana robots on the series upgraded version of "What Not to Wear" from the 21st century. Its original use was to "defabricate" clothing by making it literally disappear. Captain Jack Harkness was able to upgrade the device into a weapon, by tweaking the system, after he destroyed the robots, who tried to kill him. The weapon fired a bluish beam of energy that was capable of piercing Dalekanium armour, hence can destroy a Dalek. During the Battle of the Game Station, Jack killed a Dalek with it, but resulted in depleting the power source. (DW: Bad Wolf / The Parting of the Ways)

Jack had somehow managed to have brought this weapon along with him when he transported himself back to the 19th century and used the weapon again when the Earth was stolen by the Daleks. Apparently this time he had replaced the power source with a better one as he was able to use it at least twice: killing a Dalek and the Supreme Dalek. (DW: The Stolen Earth / Journey's End)