The Rev Dr Iain Greenshields, moderator of the General Assembly of the Church of Scotland, said the new Nationality and Borders Act makes life extremely difficult for vulnerable people seeking safety in Britain.
The Westminster Government announced its asylum plan to send refugees who cross the English Channel to the African nation, in April.
It was hoped the plans would deter others from crossing the Channel illegally.
However, a flight containing seven people was halted minutes before take-off by the European Court of Human Rights (ECHR).
Home Secretary Priti Patel has said the UK Government will not be “deterred” from progressing with the policy, with future flights already planned.
Dr Greenshields said forcing asylum seekers to go to Rwanda was an “unspeakable disgrace and a stain on our nation”.
He said: “As people flee oppression, violence, conflict and war, many unfortunately do not find the welcome or safe place they need.
“In the UK, the new Nationality and Borders Act 2022 threatens the very principle of refugee protection and offers protection on the grounds of how people arrive in the UK, rather than the war, terror and persecution a person may be fleeing from.
“The trajectory to create a web of hostile policies to make life as difficult as possible for those seeking protection continues.
“This is an unspeakable disgrace and a stain on our nation.
“Our UK Government is putting up barriers to prevent people finding the peace and safety they need, and robs them of the opportunity to contribute their skills and experience to the communities.”
“People now face the prospect of transportation to Rwanda.”
The church moderator has now urged the UK Government to have a “change of heart” on the policy.
He added: “They may feel their policy to be just and right but they dishonour God by their inaction, lack of compassion and disgraceful attempted solution to this critical situation.”
Home Secretary Priti Patel said the plans would allow those arriving in the UK “dangerously” to be relocated to “build their lives” in Rwanda.
She added: “This will help break the people smugglers’ business model and prevent loss of life, while ensuring protection for the genuinely vulnerable.
“Access to the UK’s asylum system must be based on need, not on the ability to pay people smugglers. The demands on the current system, the cost to the taxpayer, and the flagrant abuses are increasing, and the British public have rightly had enough.
“I have always said this policy will not be easy to deliver and am disappointed that legal challenge and last-minute claims have meant (Tuesday’s) flight was unable to depart.
“It is very surprising that the European Court of Human Rights has intervened despite repeated earlier success in our domestic courts. These repeated legal barriers are similar to those we experience with other removals flights and many of those removed from this flight will be placed on the next.
“We will not be deterred from doing the right thing and delivering our plans to control our nation’s borders. Our legal team are reviewing every decision made on this flight and preparation for the next flight begins now.”