Horror filmmakers such as Marcus Nispel and Alexandre Aja have talked in the past about making movies in which someone clones Jesus from the DNA in his blood, but as far as I can tell, those projects never got off the ground. Writer-director Leone Marucci, on the other hand, has a film on this very topic coming out next month, starring Christopher Walken, Christian Slater, Larry King and that girl who played Pocahontas in The New World. The film in question — which frankly doesn’t look all that good — is called The Power of Few and seems to follow several parallel storylines; the stealing of the Shroud of Turin, and the possible extraction of DNA from the bloodstains thereon, might not be all that big a part of the movie as a whole, but the trailer certainly emphasizes those elements.
You can watch the trailer below:
Update: For other examples of how this premise has been treated in books, comics, films, etc., see the ‘Clone Jesus’ entry at TV Tropes.