The Scottish Conservative leader said RT was peddling "soft-sell propaganda" in a bid to "poison our public discourse" and called for a crackdown.
Regulator Ofcom is reviewing whether RT remains 'fit and proper' to hold a UK broadcast license in light of the government's claim that the Russian government, which funds the station, is "culpable" for the nerve agent attack in Salisbury.
In an article for the Sunday Telegraph, Ms Davidson writes: "Russia Today, the state-owned, UK-based channel described the claims of a Russian link to the Salisbury attack as 'fanciful'.
"On Russian state TV, it was suggested that Britain deliberately arranged the attack in order to stoke 'Russophobia'. It is we, not Russia, who are guilty of spreading propaganda in the wake of the attacks, declares their foreign ministry, as part of an 'anti-Russian campaign'.
Ms Davidson goes on: "Even as victims lie gasping for their lives in a hospital bed in England, truth is bent beyond recognition. Russia is industrialising false information: less an Iron Curtain these days than a web of lies.
"Exploiting the very virtues we uphold - of free expression and freedom of speech - the purpose is to further corrode trust in our public realm, and weaken our society.
"So, beyond the necessary sanctions proposed by the Prime Minister this week in response to the Salisbury attack, there is also a wider response necessary. We must reject any attempt to draw moral equivalence between Britain's vigorous free media, and the highly polished counterfeit versions that Russia is promoting.
"Firstly, that means cracking down on Russia's ability to broadcast falsehoods in this country - by, for example, tougher regulation of the soft-sell propaganda of Russian Today and its Sputnik offshoot.
"That Alex Salmond, the former Scottish first minister, continues to act as a frontman for RT is a shameful stain on his reputation. I hope we can soon pull the plug on it."
Appearing on ITV's Peston on Sunday programme, the SNP's Westminster leader insisted Mr Salmond was a "private citizen" and refused to criticize the former nationalist leader, but made a point of highlighting the lack of press freedom in Russia, saying: "We couldn't have this conversation if we were on Russian television".
Asked whether Mr Salmond's producer and co-host, the former SNP MP Tasmina Ahmed-Sheikh, should remain on the party's national executive committee as equalities convener, Mr Blackford said the position was elected and unpaid, but highlighted abuses of human rights in Russia.
Mr Blackford called for further financial sanctions on the Russian government and its associates, including a crackdown on Scottish Limited Partnerships—shell companies that have seen millions of pounds from the former Soviet countries laundered using Scottish addresses. He called the Salisbury attack "effectively an act of state terrorism".
In her article, Ms Davidson goes on to call for greater protections for free speech in the UK, arguing that proposals to force British newspapers that do not sign up to a new state-approved regulator to pay the costs of complainants in data protection cases would be "disastrous".
"They wouldn't be able to pay, so, most likely, editors would simply drop investigations, for fear of being taken to court," she says. "They might feel compelled to print apologies even when they had written something correct."