The Scottish Conservative chief spoke out as the GMB union put forward a motion backing the renewal of the weapons system to the Scottish Trades Union Congress (STUC) annual congress in Dundee.
While Scottish Labour voted against renewing Trident at its conference last year, the GMB motion warns a “failure to progress the Trident successor programme will have devastating consequences” for jobs and could see local economies “decimated”.
The motion states scrapping Trident, which is based at Faslane on the Clyde, would mean “prosperity and hope of a better future will fade away, replaced by low wages, zero hours contracts and a spiral into poverty”.
“This is not a future any self-respecting trade union should contemplate supporting for decent hard-working people.”
Ms Davidson said: “I have met and listened to many traditional Labour supporters who see the common sense in renewing Trident. They are worried about the direction the party is now taking.
“My message to them is that me and my team will stand shoulder to shoulder with you on this issue.
“Together we can make the case for preserving Britain’s security and for protecting thousands of Scottish jobs.”
While she said Labour supporters “used to be able to trust their party on this”, she said they were now in a “total mess” on Trident.