In a video posted on Tsargrad TV's social media channels, television host Andrei Afanasyev encouraged gay people to compete for the flight.
In the clip, Afanasyev says "the staff of Tsargrad TV support this initiative" and that California is a sympathetic home to Russian LGBT people.
He added: "This is not a joke.
"We really want you to return there, where you can openly submit to your sins."
The video's description which includes emojis of a plane and a sick face states the rules for the competition: "For this you need to have a medical certificate that confirms sodomy or other forms of perversion, and also contact our host."
The video message was posted earlier this week on Saint Petersburg-based social network VK, Russia's most popular website and has since gained over 34,000 views.
Konstantin Malofeev, the channels general producer said the channel is "a platform and voice of the Russian Orthodox majority". The channel claims an audience of about a quarter of the Russian population.
He has said he views his channel as the equivalent of America's Fox News channel.
Tsargrad TV also calls itself Constantinople, after the ancient centre of Eastern Christianity and capital of the Byzantine Empire.
While some people have expressed their interest in taking up the offer under the posted video it is unclear how serious they are, if they have contacted the presenter or if anyone from the channel has contacted them.
