It adopted the new policy at an annual meeting in Belfast on Friday.
The measure will not prevent anyone from attending worship, coming into church, receiving communion, or having access to pastoral care, a spokesman said.
He added: "On many issues the Church provides guidance to our ministers and elders in Kirk sessions and we wanted to consider what a credible profession of faith means for same-sex couples who want to become communicant members of the Church.
"The same principle also applies to everyone, regardless of background or circumstance and those who want to baptise their children."
Earlier in the week, the church voted to loosen its ties with the Church of Scotland because of its more liberal attitude towards same-sex relationships.
The head of the Church of Scotland (moderator) will no longer be invited to the annual meeting of the Presbyterian General Assembly in Belfast.
Last month the Church of Scotland took a step towards allowing ministers to conduct same-sex marriages.
Its General Assembly asked a committee to draft church law on the issue.
The Church of Scotland is considered the mother church of the Presbyterian Church of Ireland.
Presbyterians in Ireland have also agreed their moderator, the Rev Dr Charles McMullen, should meet Pope Francis when he visits Dublin in August.
The Presbyterian Church in Ireland is the largest denomination in Northern Ireland.
Earlier in the week its General Assembly agreed to strongly oppose any legislation which allows assisted suicide and/or euthanasia.
Lindsay Conway, secretary of the Council for Social Witness, said the Assembly needed to be aware of the "slippery slope principle", warning that in the Netherlands mental health issues were now grounds for assisted suicide and euthanasia.
The Republic's Government was also urged to keep to its promises that abortion will be rare in the state and that children with disabilities will not have their lives terminated.
The Presbyterian Church opposed repeal of the Eighth Amendment of the Constitution which outlawed abortion in most cases ahead of the May 25 referendum.
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