She wants those who voted against independence in the 2014 referendum to cast their second vote in support of her party, arguing it is “the intelligent vote for the union”.
Ms Davidson has also called for supporters who backed other unionist parties at the general election to try to stop the SNP to return to the Tories.
Voters will elect 73 constituency MSPs with the first-past-the-post system and use their second vote to elect 56 list MSPs by an additional member system.
Only three of the 15 seats currently held by the Tories are constituency seats.
Speaking at the UK party conference in Manchester, the Scottish leader will say: “In May, many Scottish Conservative voters supported other pro-UK parties in the hope of stopping the SNP.
“I can tell you there are two reasons why this will not happen next year.
“Firstly, because Labour and the Lib Dems now seem to be embarrassed by their support for Scotland’s place in the UK.
“And secondly it’s because next year every single vote counts.”
She will add: “As the head of our campaign, I have made it clear to my team that I want to target the regional list vote next year.
“For so long as the SNP refuses to rule out another referendum, our message for voters looking to cast that second vote is clear. Whichever party you support, use that vote intelligently.
“If you’re one of the two million people who voted No in last year’s referendum, use it as your intelligent vote for the Union.
“Be assured of this - every cross in the Scottish Conservative box is a vote to promote Scotland’s place as part of the United Kingdom we built. Every vote for the Scottish Conservatives will help return a Conservative MSP.”