Cardinal Keith O'Brien was named in the controversial category at Stonewall's annual award ceremony in London.
The charity said the move was voted for by 10,000 supporters and came after the cardinal went "well beyond what any normal person would call a decent level of public discourse" over the last year, which has seen heated debate over plans to introduce gay marriage in Scotland.
But the Catholic Church criticised the charity's award, saying it revealed "the depth of their intolerance" and a willingness to demean people who do not share their views.
The row came after Scottish Conservative leader Ruth Davidson picked up a politician of the year gong from the equality group.
Ms Davidson was awarded the title in recognition of her becoming the first openly gay leader of a major UK political party.
But she criticised the bigot of the year category, saying it was "simply wrong" to use such terminology.
Ms Davidson, who attended the ceremony presented by broadcaster Gok Wan, said: "There are many voices in this debate and just as I respectfully express my sincerely held belief that we should extend marriage to same-sex couples, I will also respect those who hold a different view."
A spokesperson for the Catholic Church said the announcement "reveals the depth of their intolerance and willingness to attack and demean those who don't share their views."
The church also called into question Government funding of the organisation.
It said: "Numerous public bodies give sizeable financial donations to Stonewall including the Scottish Government, these intolerant and intimidatory tactics should mean that this funding is now questioned and examined as a matter of urgency."