Mr Coburn claimed he had been issued with a membership card by the party "several weeks ago".
But Scottish Conservative leader Jackson Carlaw made clear he could not back an application from the controversial ex-MEP, stating that some of his previous comments were "incompatible with membership".
In 2015, when he was an MEP, Mr Coburn apologised after he likened Humza Yousaf, a member of the Scottish Government, to the convicted terrorist Abu Hamza.
Mr Carlaw said on Twitter: "I understand David Coburn has applied to join the Scottish Conservatives.
"As leader I have to make it clear that past public comments by him are incompatible with membership & I cannot and will not support his application."
But Mr Coburn, a former Scottish Ukip leader, said he had a party membership card that had been "issued several weeks ago with an acceptance letter and a membership number".
He tweeted: "I applied for membership @ToriesScots recently and was accepted. I am now a card carrying member with membership number etc."
Mr Carlaw responded: "As part of the online process to join the party, anywhere in the UK, it clearly states that membership is subject to confirmation.
"Mr Coburn's membership has been rejected and any sum paid by him as part of that online process, will be refunded."
Mr Coburn was Scotland's first elected Ukip parliamentarian after winning one of the country's six MEP positions in 2014.
He left Ukip in 2018 and joined the Brexit Party but did not seek re-election to the European Parliament in 2019.
Mr Yousaf, now the Justice Secretary, said if Mr Coburn has been allowed to join the Tories this would be "proof that Islamophobia is not just tolerated but systemic within the Conservative Party".
In reaction to the speculation on social media, Mr Yousaf said: "The man who called me 'Abu Hamza' as an Islamophobic slur has surely not been allowed to join the Tories, has he?!"Serious questions to ask of Conservatives if they have, would be further proof that Islamophobia is not just tolerated but systemic within the Conservative Party."