Members of the society, which includes 11,000 practising lawyers, triggered a non-binding vote earlier this year that overturned a decision by the society's board of governors to accredit Trinity Western's new law school in the Fraser Valley.
As a result of that, in June the law society said members would vote on a resolution that declares "the proposed law school at Trinity Western University is not an approved faculty of law for the purpose of the Law Society's admission program."
The law school at the faith-based university is set to open in 2016. Critics oppose the plan because Trinity Western students must sign a Christian covenant that states sexual relations are to be confined within the bounds of a marriage between a man and a woman.
Critics say the policy is discriminatory against people in LGBT relationships.
The Law Society of Upper Canada in Ontario has voted against approving the law school and the Nova Scotia Barristers' Society has granted conditional acceptance if the school changes the covenant for law students or allows them to opt out.
Trinity Western is legally challenging those decisions in court.
The Law Society of B.C.'s resolution is binding if the referendum meets two conditions. First, at least one-third of the society's members need to have voted in the referendum and at least two-thirds of those voting need to vote in favour of the resolution.
By Wednesday, Oct. 22, the society said, 6,690 members had voted and met the one-third membership -vote threshold.
The results of vote will go to the Law Society of B.C.'s board of governors, known as benchers, on Friday for final approval if the resolution passes.