At the General Assembly this week, members voted to send the issue out for further debate and defer a final decision for at least a year.
The Kirk said the proposal would not change its stance on gay marriages inside churches and it would continue to reject the validity of same sex marriages.
It comes after the Assembly decided to allow people in same- sex civil partnerships to be called as ministers and deacons.
That meant the Church maintained its traditional view on marriage but would allow individual churches to appoint a minister who was in a civil partnership.
The proposal of ministers in gay marriages will now be debated at presbyteries and they will return their votes by the end of the year.
Convener of the Church's Theological Forum, the Very Revd Prof Iain Torrance said: "Out of a pastoral concern for the whole Church, the General Assembly decided to pass this overture to the presbyteries, who will report to the Assembly in May 2016."
Free Church Moderator Revd David Robertson said: "The Church of Scotland has adopted two contrasting positions - that it is acceptable for ministers to be in gay marriages, but not so for parishioners. The whole thing is totally confusing.
"We don't understand what's going on in the Church of Scotland, and suspect the vast majority of the Scottish public don't have a Scooby either.
"We believe that Scotland needs the guidance of a national church rooted in the teachings of the Bible, irrespective of public opinion and pressure to conform."