A "fact check" produced by Australian Broadcasting Corporation News and RMIT concluded that then Attorney-Geneeral George Brandis' claim in November 2017 that Australia runs the most generous refugee program per capita in the world was misleading. Various complexities of the data are examined in the article, which says that Australia's level of refugee recognition is small compared to other wealthy nations (as well as poorer ones).
I also checked the article that was the source for the paragraph above, the relevant parts of which I quote:
Senator Brandis's claim is misleading.
Australia's "offshore" refugee and humanitarian resettlement program — that is, people facing persecution or violence elsewhere who are selected by the Government to come to Australia — is among the most generous in per capita terms, although it is currently not the most generous. That title goes to Canada.
In 2016, Australia resettled 27,626 people from elsewhere, a rate per 1,000 of 1.139, compared with 46,702 people resettled in Canada, a rate of 1.286.
However, this represents only a small part of the global response to the problem of displaced people, which according to the United Nations Refugee Agency has risen to an "unprecedented" level.
In addition to "offshore" resettlement, in 2016, 6,567 people arrived in Australia seeking asylum who were recognised as refugees.
Australia's level of refugee recognition is relatively small compared to other wealthy nations (and also many poorer countries).
In 2016, for example, 443,210 were recognised as refugees in Germany and 532,735 in Uganda.
Sweden and Norway, which both have smaller populations than Australia, recognised 68,090 and 12,147 refugees respectively in 2016.
When figures for refugee recognition at home and resettlement from abroad are combined, Australia slips well down the list in per capita terms.