The Campaign for Nuclear Disarmament group within the party is meeting in Glasgow today to rally support for opposition to the policy change, which will be debated at national conference in Perth in October.
But Mr Robertson has produced more data from a poll commissioned by his parliamentary group at Westminster to inform the party's defence policy review.
This shows 63% of voters think Scotland would be safer by remaining part of Nato, compared to just 5% who believe it would be safer if it left the alliance.
Those who said they did not know counted for 11%, while 21% believed remaining in Nato or leaving would make no difference to the safety of the country.
Mr Robertson, the Westminster group leader and MP for Moray, who is proposing the updated SNP defence policy said: "With an agreement to withdraw Trident from Scotland, I think we should be willing to work with our neighbours and allies.
"All of our North Sea neighbours consider Nato to be the cornerstone of their defence and security policy and they should be confident that Scotland will work with them.
"These poll findings underline the overwhelming degree of public support for an independent Scotland working within Nato. The strong agreement among women that remaining in Nato is safer is noteworthy.
"This follows details showing 75% public support for an independent Scotland remaining in Nato." Mr Robertson's conference motion proposes: "An SNP Government will maintain Nato membership subject to an agreement that Scotland will not host nuclear weapons and Nato continues to respect the right of members to only take part in UN-sanctioned operations."
In the absence of such an agreement, it adds, it would revert to the previous policy of joining the Partnership for Peace group of countries.
Cumbernauld and Kilsyth MSP Jamie Hepburn will be proposing no change to the current policy and has attracted the support of several Holyrood colleagues.
As revealed in The Herald this week, a paper being discussed at today's CND group meeting gives warning that continued Nato membership will make it harder to remove the Trident base at Faslane. It points to Germany, the Netherlands and Belgium which have all asked, without success, for nuclear weapons to be removed from their soil.
The paper also claims the policy switch would make the SNP "look cynical and lacking in moral courage".
Although the YouGov poll of more than 1000 adults showed support for staying in Nato across the political spectrum, SNP voters were the most sceptical of the benefits of the alliance.
On the issue of being safer staying in Nato, that view was held by 83% of Conservative voters, 70% of Labour voters, 68% of LibDem voters, and 50% of SNP voters. Mr Robertson said: "Being able to determine your own defence and security policy is one of the most significant advantages of independence. We should make better decisions in Scotland and a conventional non-nuclear Scotland working fully with our neighbours is the best outcome."
The proposals will be debated at the SNP National Conference in October.
Bill Ramsay, secretary of the SNP's CND group, said the meeting at the STUC in Glasgow would normally attract "a couple of dozen people" but today's event was expected to attract far more interest.
He said of Mr Robertson's claims: "The wording of this poll suggests that without Nato, Scotland faces some unspecified threat, which is utter nonsense. Angus need to come out and argue his case instead of hiding behind dodgy polls."