The debate follows an earlier vote to allow clergymen and woman who were in civil partnerships to be appointed as ministers.
Assembly members may not make a decision on ministers in gay marriages today and instead could take a number of other options.
If there is no vote there could be an order for a church commission to produce a report on the issue to be discussed at a future meeting.
It's the first time the Kirk has officially discussed appointing ministers in same-sex marriages despite much heated debate.
The Church says the vote is not on the issue of gay people getting married in church and that the Kirk is still against this.
Supporters of allowing ministers in gay marriages say it's time for the Church to be inclusive but opponents say gay marriage goes against the Bible.