Addressing his party's spring conference in Aberdeen, Rennie said he wanted to amend justice legislation at Holyrood to scrap the practice after a surge in its use.
The call for change came after delegates unanimously passed an emergency motion demanding full recording of stop and searches to prevent their abuse, which credited the Sunday Herald's reporting of the issue.
Specifically, it referred to a admission by Chief Constable Sir Stephen House, in a Sunday Herald interview, that some stop and search records could be made up by police officers. If backed by MSPs, the change would mean all stop and searches would be underpinned by law, and would require reasonable suspicion of criminal activity.
At present, around 74% of stop and searches in Scotland are "non-statutory", or voluntary.
Police officers ask people for consent to search them, but those searched are usually unaware they can refuse.
The Scottish Centre for Crime and Justice Research recently reported 1860 searches were being conducted by Police Scotland each, or 131 per 1000 people, twice the rate of the Metropolitan Police.
It concluded non-statutory stop and search raised "concerns in relation to procedural protection, consent, proportionality and human rights", and recommended they be phased out.
These searches are supposed to be "intelligence-led, proportionate and respectful".
The LibDems' amendments to the Criminal Justice (Scotland) Bill would "put stop and search on a regulated footing", Rennie said.
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 with 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."
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 from April to December 2013, according to Police Scotland. Searches undertaken to detect firearms yielded a positive result in 37% of cases, with 166 "firearms or associated items" recovered.
LibDem justice spokeswoman Alison McInnes said there have been "deeply worrying" revelations about the power.
"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."
The speech had been billed as part of Rennie's "sunshine strategy", a more positive approach to the referendum, and was peppered with the word "positive" and relatively few digs at the SNP.
Rennie also called on the SNP to use extra funding from the UK Government to extend free childcare. With the European elections on May 22, Rennie urged the party to work for the re-election of the sole LibDem MEP in Scotland George Lyon, who he called "too good to lose".