Mr Rennie wants to amend the Criminal Justice (Scotland) Bill, currently passing through Holyrood, to scrap the practice, following concerns over increases in its use.
The change, if backed by a majority of MSPs, would mean all stop and searches would be underpinned by legislation and would require reasonable suspicion of criminal activity.
At present, over 70% of stop and searches carried out are voluntary. These searches are also required to be "intelligence-led, proportionate and respectful", according to the Scottish Police Authority (SPA), but officers do not have to meet certain legal requirements.
The Lib Dems' amendments will "put stop and search on a regulated footing", Mr Rennie said as he addressed the Scottish party's conference in Aberdeen.
This would "keep the police focused on those they suspect of crime and confirm the freedoms of the innocent", he added.
"My head tells me the best policing is by consent. My heart tells me children deserve better. Scotland needs a liberal party, the Liberal Democrats, because on police centralisation we were alone at first; on corroboration people agreed we were on to something; and now stop and search we have a fresh challenge.
"No liberal party would act like this government. No liberal party would take a wrecking ball to the justice system like they have."
Mr Rennie had focused on the stop and search powers at First Minister's Questions in Holyrood last Thursday.
He accused Alex Salmond of being "casual and complacent" about a fourfold increase in the use of stop and search.
Some 519,213 stop and searches were conducted between April and December 2013, according to Police Scotland figures.
Searches undertaken to detect firearms yielded a positive result in 37% of cases, with 166 ''firearms or associated items'' recovered.
Almost 37% of alcohol-related searches were positive and 61,541 recoveries were made.
Lib Dem politicians and activists condemned the current approach to stop and search just before Mr Rennie announced his plan to force changes.
They unanimously backed a motion raising concerns about Police Scotland's use of the power.
The party called on the Scottish Government to ensure full and proper records are kept so the policy is not "open to abuse".
Lib Dem justice spokeswoman Alison McInnes, a North East MSP, said there have been "deeply worrying" revelations about the power.
She said: "There is no robust evidence showing a link between a rise in stop and search and the record low on crime. Indeed there is a very real risk that the recording of positive results upon which the policy is justified is itself, at best, inconsistent, and at worse being manipulated.
"Used appropriately, stop and search is an important part of the policing toolkit. But unfettered, under the radar, the system is open to all manner of abuse."
Mr Rennie also used his speech to call on the Scottish Government to use extra funding from the UK Government to extend free childcare even further.
He wants the SNP administration to extend its free childcare proposals to cover 40% of Scotland's two-year-olds, starting with the most vulnerable children.
''Thanks to the UK budget and the improving economic conditions the Scottish Government now has the money they need to implement the childcare package in full," he said.
''I want John Swinney to use the extra money he has received in that budget to fully match the excellent work south of the border on early education and childcare."