The group, Our Islands Our Future, lodged a petition with the Scottish Parliament on 29 April, and have collected some 1,177 in support of their proposal.
"Whether you live in Shetland, Orkney or the Western Isles, you will know that your part of the world was once in Norway and still has its own traditions and culture which set it apart from the rest of what is now Scotland," Malcolm Lamont, from Lerwick in the Shetland Islands wrote introducing the petition.
The campaigners want a separate referendum for their islands on 18 September 2014, when Scotland is itself voting on whether to continue as part of the United Kingdom.
"A referendum will soon be held on whether Scotland should be an independent country. What better time to decide the status of each of these island groups?" Lamont wrote in the petition.
"Many believe there is a case for independence - for Shetland, for Orkney, and sometimes the idea is also heard in the Western Isles. Others believe there is a case for remaining part of the UK even if Scotland leaves."
Orkney and Shetland were both controlled by Norway from the 9th century until they was transferred to the Scottish King James III in 1468 and 1472 respectively.
The Western Isles were transferred to the Kingdom of Scotland in 1266 as part of the Treaty of Perth with Norway.
Catriona Murray, the secretary of Our Islands Our Future, said that the group did not see a return to Norwegian rule as an option.
"We discussed that we should have an option where we ask people if they want to become part of Norway," she told NRK. "But we chose to walk away from it, since very few on the islands support this."
However, she said a vote on joining Norway could come once the islands vote for independence.
"If the Scottish government lets us get a vote, and there is increased support for Norwegian membership after that, I think people will get to vote on it," she said.