The General Synod of the church voted that a change to its Canon law governing marriage should be sent for discussion to the church's seven dioceses.
A further vote will take place at next year's synod.
It means that gay Christians from any Anglican Church can now ask to be married in a Scottish Episcopal Church.
The proposal would remove the doctrinal clause which states that marriage is between a man and a woman and there would be a "conscience clause" for those who would not want to conduct a same-sex marriage.
The synod vote today received support from five of seven bishops and 69 per cent of the clergy - indicating that it has a good chance of succeeding when it returns next year.
If passed, it would mean Scottish Episcopals would become the first major church in the UK to marry gay and lesbian couples in church.
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