The Oscar winner was unveiled as the new Time Lord last year (13), taking over from Matt Smith, and he was introduced to viewers in a special Christmas episode of the sci-fi hit in December (13).
Capaldi's first full episode as the time traveller is due to be broadcast next month (Aug14), but a rough cut copy has been posted on the Internet.
Titled Deep Breath, the early edit is in black and white and is yet to have any special effects added.
However, writer Steven Moffat is urging Doctor Who fans to resist the temptation to watch the leaked copy, saying, "Someone has screwed up. The launch of a new Time Lord is the most exciting but the most dangerous moment in the show - so let's keep Peter Capaldi's first episode special."
The leak is the latest blow to Bbc bosses, who were already reeling from the news last week (beg07Jul14) that the scripts for five new Doctor Who episodes have been posted on the Internet.
It is believed the rough cut of Deep Breath has leaked from the same source.