Party leader Douglas Ross said the pledge to repeal the legislation would see the Scottish Parliament “overturn the dangerous threats to freedom of speech”.
He said other opposition parties “did not do enough” to stop the bill from becoming law, calling for a cross-party alliance to repeal the Bill in the next Parliament.
The Bill, which aims to consolidate and extend existing hate crime law, was passed 82 votes to 32 on Thursday after months of debate and multiple amendments.
Mr Ross said: “Backed by Labour, the Lib Dems and Greens, the SNP have passed one of the most extreme and outrageous laws in the history of the Scottish Parliament.
“We opposed the SNP’s Hate Crime Bill and our manifesto will pledge to repeal it.
"We will seek to overturn the dangerous threats to freedom of speech and our fundamental rights that [justice secretary] Humza Yousaf refused to remove. The SNP Government has no place criminalising what people say in their own homes.
“Other opposition parties did not do enough to force the SNP to fix this shambles of a Bill, but I now ask that they take this moment and reconsider. Work with the Scottish Conservatives, stand up for free speech and join us in including a pledge to repeal this Bill.
“The passing of this Bill shows the clear danger of an SNP majority and why the Scottish Conservatives are determined to stop them in the coming election. Without enough opposition MSPs to challenge the SNP, they would pass even more oppressive bills.”
Mr Ross also announced a pledge to include ‘Suzanne’s Law’ into their plans to bolster protections and rights of victims of crime in Scotland.
Such a move would give authorities the power to refuse parole or temporary release to murderers who fail to disclose the location of their victim’s body.
Mr Ross said: "Killers should be given a simple choice – fully disclose what they have done with remains or stay locked up until they do so.
"In some of these appalling cases, killers appear to take a perverse pleasure in prolonging the suffering of grieving relatives.”