St Margaret's Children and Family Care Society in Glasgow has been told it could lose its charitable status unless it changes its adoption criteria.
The Office of the Scottish Charity Regulator (OSCR) reviewed the practices of the charity after a complaint from the National Secular Society and found it was operating in breach of the Equality Act 2010.
St Margaret's gives greater priority to prospective adoptive parents who are a couple, Catholic, married for at least two years and wish to adopt within the framework of the Catholic faith, the report said.
Lower priority is given to enquirers who have been married for less than two years, couples in civil partnerships, single people and married couples who do not wish to adopt within the Catholic faith, the OSCR said.
The report reads: "The charity's preferred criteria prioritise couples who have been married for at least two years: marriage is not available to same-sex couples and this constitutes direct discrimination.
"Since it is discriminating in breach of equality law, OSCR finds that access to the benefit the charity provides in assessing prospective adoptive parents is unduly restricted.
"OSCR also finds that this discrimination causes disbenefit to same-sex couples.
"For these reasons OSCR finds that the charity does not provide public benefit and it therefore fails the charity test."
St Margaret's has until April 22 to comply with the Equality Act, OSCR said.
The Scottish Government announced plans to legalise same-sex marriage in July following a consultation which attracted 80,000 responses.
The proposals have received cross-party support in Holyrood and the Government is continuing to seek views on its Marriage and Civil Partnership (Scotland) Bill.
OSCR's head of registration, Martin Tyson, said: "We acknowledge the valuable service provided by this charity, but the fact is that all charities must comply with the law, including the Equality Act 2010. Where we find this is not the case, we have a duty to act.
"We have carefully considered the details of this case, and the legal position is clear - the charity must take steps so that it does not discriminate unlawfully and can pass the charity test. This case was complex and we discussed matters at great length with the charity's trustees. We hope that the charity will respond positively and take the necessary action so that it remains in the Scottish Charity Register."
St Margaret's Children and Family Care Society is partly funded by the Catholic Church and the trustees of the charity include bishops from dioceses in the west of Scotland.
Alistair McBay, Scottish spokesman for the National Secular Society, said: "This kind of crude discrimination is no longer acceptable in our society - and that goes double where the discrimination is, in effect, being largely financed by the public purse.
"Arguably more important than depriving gay couples of adoption is that St Margaret's policy restricts the pool of adoptive parents, including gay parents, some of whom the regulator acknowledges have special skills that would be especially appropriate with hard-to-place children.
"If St Margaret's wishes to continue to provide services, it must remove these provisions from its constitution - this will be in the children's best interests. In England, some of the Catholic agencies complied and are now providing their services to everyone without prejudice.
"We hope that St Margaret's will continue to fulfil its valuable role, even if it has to sever its connection with the Catholic Church."
The Scottish Catholic Church said it will respond to the report in due course.