Searching replacement for broken plug
I took a look on Mouser and Digikey but I didn't see anything that looks remotely like that connector.  Farnell (UK) sells a cable (€13,53 delivered to DE) that might have the same connector.  I'm not sure the connector is the same though (here's the datasheet).
Honestly, your best option IMO is to get a (used) replacement for either the cable or the cable and board from ebay1.  Cable with the webcam board: US$10.  Or just the cable: CA$39 or US$17.  Going the ebay route is probably cheaper too since you're looking at probably US$5-US$8 minimum for shipping from a distributer like Mouser.
1All prices above include shipping.  I am in no way affiliated with any of the sellers I linked to.