Mr Salmond's weekly show on the Russian-state funded chanel made its debut today with deposed Catalan President Carles Puigdemont among the guests. But the ex-First Minister has come under fire over his decision to host a show on the Russian-state funded channel amid claims it is "propaganda" vehicle for Vladimir Putin's regime and the Kremlin.
Mr Rennie raised the issue today's during First Minister's Questions at Holyrood as he grilled John Swinney who was standing in for Nicola Sturgeon.
"We should remember this is the TV channel that seeks to undermine western democracy and ignore human rights abuses at home," Mr Rennie said.
Estonian ambassador Tiina Intelmann told Holyrood's External Affairs committee this morning that Russia Today is "Kremlin-backed propaganda."
Mr Rennie added: "It should turn our stomach to know that a former First Minister of this country is giving it credibility and legitimacy by launching this show this very day.
"Scotland's reputation abroad has been damaged. Countries - small countries - particularly along the Russian border will be deeply concerned by this decision. Alex Salmond does not speak for Scotland on this."
Mr Rennie today questioned whether Mr Salmond was a "fit and proper person" to be chairman of the firm which owns the Scotsman newspaper. The ex-First Minister is currently part of bid be chair of the board of Johnston Press which owns the Scotsman.
"Newspaper regulation is devolved," Mr Rennie said.
"So it's reasonable to ask whether Alex Salmond would be a fit and proper person to own the Scotsman when he is being paid by President Putin's propaganda channel."
Mr Swinney was asked what the Scottish Government is doing to "actively distance itself" from Alex Salmond.
The Deputy First Minister responded that Ms Sturgeon said last week that she would have advised Mr Salmond against broadcasting the show on Russia Today, but was not asked.
But Mr Swinney pointed out that Liberal Democrat UK leader Vince Cable has previously appeared on Russia Today
He said that today's debut show had guests from the Labour party and Tories.
He added: "The whole debate has been struck by a stinking reek of hypocrisy from every other political party on this question."