Did Rudy Giuliani say "it's highly likely that all these people that have contracted the China Virus got it from having sex with barnyard animals"? No, there's no evidence he ever said that. Searches on Google and Twitter turned up no instance of such a quote attributed to Giuliani, who has tested positive for COVID-19.
The claim appeared in a Facebook post (archived here) published by "The Salty Liberals" on December 7, 2020. The post included a short message, which read: "I cannot confirm or deny this." It also included what looked to be a Giuliani tweet, dated October 20, 2020. The purported tweet read:
I think it's highly likely that all these people that have contracted the China Virus got it from having sex with barnyard animals.
This is what the post looked like at the time of writing:
(Source: Facebook screenshot taken on Mon Dec 7 19:20:20 2020 UTC)
Giuliani, who is Donald Trump's lawyer, has tested positive for COVID-19. On December 6, 2020, the president wished him well:
.@RudyGiuliani, by far the greatest mayor in the history of NYC, and who has been working tirelessly exposing the most corrupt election (by far!) in the history of the USA, has tested positive for the China Virus. Get better soon Rudy, we will carry on!!!-- Donald J. Trump (@realDonaldTrump) December 6, 2020
For his part, Giuliani thanked his supporters and expressed confidence in a quick recovery:
Thank you to all my friends and followers for all the prayers and kind wishes.-- Rudy W. Giuliani (@RudyGiuliani) December 7, 2020
I'm getting great care and feeling good.
Recovering quickly and keeping up with everything.