Ms Davidson, who is a member of the Church of Scotland and the first openly gay leader of the Scottish Tories, said: "The Church has come a long way very fast.
"It still has a long way to go but it's absolutely going in the right direction. I'm very hopeful I'll be able to see gay church weddings in my lifetime."
Stressing the decision lies with the Church of Scotland's governing body, the General Assembly, she added permitting same sex marriages is an "issue that the Church will take in its own time".
The leader of the Scottish Conservatives for more than four of her five years as a Member of the Scottish Parliament, Ms Davidson also claimed she is willing to put pressure on Northern Ireland politicians so they follow the rest of the UK in legalising same-sex marriage.
Ms Davidson said: "I've been invited by Amnesty International to give their annual Pride lecture in Belfast this year, to talk about the situation in Northern Ireland, and I'm going to take my Irish partner with me."
"I think we've come a really long way - but we shouldn't forget there's still a part of the UK where our citizens do not share the same rights, just a few miles away."
A Church of Scotland spokesman said: "The Church has asked its Theological Forum to report on the theology of same-sex marriage and it is likely that this report will be considered at the General Assembly of 2017.
"It would be premature to try to predict either what the report will say or how the Assembly will decide."