Chief Minister Andrew Bar has offered to fill out a proxy vote for anyone who wants to authorise him to vote in the same-sex marriage survey on their behalf.
Mr Barr told the ACT parliament that he would stand in as what the Australian Bureau of Statistics is calling a "trusted person", and vote for people who could not vote for themselves.
The bureau says if someone can't access their survey form - if, for example, they are overseas - they will be able to authorise someone whom they trust to complete the survey form on their behalf.
The trusted person should be specifically authorised, they should also know how the voter wanted to vote and fill the form out accurately. And someone could not self-declare themselves as a trusted person, according to the bureau.
Mr Barr said he was happy to be a "trusted person" for anyone, although he implied his vote would, in any case, be yes.
The Liberals' Nicole Lawder, who supports same-sex marriage, said she was horrified by Mr Barr's "insensitive" comments, given that many people with disabilities genuinely needed someone to help them with their vote. Mr Barr was making the light of their situation, she said.
Asked later about his offer to vote, he said he had been contacted by many people overseas who feared the "highly unusual" postal survey process would exclude them.
"The 'trusted person' or proxy voting process could allow those people to participate," he said. "I am happy to act in that role for anyone who wants to guarantee a 'yes' vote."
The Greens' Caroline Le Couteur asked Mr Barr what help the ACT could offer the bureau of statistics to contact homeless people in places such as the Early Morning Centre or St Vincent De Paul's night patrol so they could vote.
Mr Barr said the government would work with the bureau to ensure people of no fixed address could vote in the "voluntary non-binding postal vote survey".
"This is clearly an appalling process to seek to find the community's views on this matter. It's hurtful and divisive and it's excluding a large number of Australians from participating," he said.