The Scottish Conservative leader, who has been under attack from the SNP and Labour over the issue, said that if she failed to do so she would be guilty of “gross hypocrisy”.
Ms Davidson, who was branded a “disgrace” by Ms Sturgeon for supporting the policy, said Holyrood had powers which could be used to offset the UK welfare reforms.
The controversial policy caps child tax credit support at two children. Women can claim tax credits for a third or subsequent child if the conception was the result of a rape, or if they were in a coercive relationship.
However, the onus is on the mother to prove the claim by filling out an eight-page form.
Ms Davidson spoke out after Ms Sturgeon challenged her to “break her silence” and condemn the policy.
The First Minister said: “Despite her claims to be an upfront, straight-talking politician, so far Ruth Davidson has hidden behind a Tory spokesperson as her party continues to defend the punitive and inhumane policy.”
The Tory leader said the Scottish Parliament has the power to create a new Scottish-only benefit, following the passage of the Scotland Act, and called on the SNP and Scottish Labour to set out their position.
She added: “We support the exemptions which the UK Government has put in place on restrictions to child tax credits, and we want to see the UK Government implement them in the most compassionate way possible. That work is on-going.
“The SNP has said it opposes the two-child policy on tax credits, so it now has a choice to make.
“At Holyrood, we now have the power to create new benefits. So the Scottish Government could, if it wanted, propose a new benefit to provide funding for families with more than two children.
“Of course this would have to be paid for, but if the SNP Government believes this to be of such importance, then it can act.
“However, if Nicola Sturgeon simply wants to use this to complain about the policies of the UK Government - and not act at Holyrood when she has the power to do so - then she leaves herself open to the charge of gross hypocrisy.”
Meanwhile, Kezia Dugdale, the Scottish Labour leader, has written to Ms Davidson to challenge her to stand up to the policy which she said “should shame every single Tory MSP”.
The reform has caused an outcry north of the border and a demonstration against it was held in Glasgow’s George Square on Thursday night.
The SNP MP Alison Thewliss responded to Ms Davidson’s challenge by saying she had become “completely isolated and desperate” in her attempts to defend the policy.
She added: “It takes a special kind of twisted logic for the Tory leader in Scotland to call for the Scottish Parliament to protect families from the vindictive policies of the Tory Government in Westminster.
“Ms Davidson fails to mention that people in Scotland already pay our taxes to the UK Government for a social security system that should be fair and there when we need it.
“If Ruth Davidson wants the Scottish Government to mitigate yet more Tory cuts, will she also call on the Tory government to pass on Scotland’s share of the pounds12 billion ‘savings’ they intend to make through those brutal welfare cuts?
“The fact is, this policy is unfair everywhere - and should be scrapped across the whole of the UK. Rather than back those calls, Ruth Davidson instead wants people in Scotland to pay an ever-increasing ransom to the Tories at Westminster to protect people on low incomes from ever-more disgraceful Tory policies.”