It would follow the lead of Northern Ireland, where a publicly-funded, online tracking service allows motorists to check where the cheapest fuel in their area is.
It has forced Northern Irish pump owners to keep their prices competitive.
In Scotland, however, the price for a litre of petrol and diesel has risen beyond £2 in some parts of the country.
Mr Rennie’s call came as protesters target key Scottish roads as part of a UK-wide demonstration over rising fuel prices.
Two tractors caused long tailbacks on the A92 towards Aberdeen on Monday, while further protests occurred at the Kessock Bridge in Inverness.
Police officers also say they cautioned two motorists on the M8 near Newbridge, Edinburgh, on Monday morning for trying to enforce a “go slow” zone.
It is understood further protests could happen if fuel prices continue to rise.
In his letter, Mr Rennie wrote: “Fuel prices are continuing to rise and we must take action now to help Scottish motorists facing increasing costs.
“The Northern Ireland price check, which is run by the Consumer Council, is an excellent model that helps to tackle rising petrol prices.
“This model has contributed to motorists in Northern Ireland paying 35p less [per litre] than Scottish motorists in June.
“The checker is publicly funded and works by letting motorists know exactly how much they should be paying for fuel.
“This allows consumers to avoid more expensive suppliers.
“The checker helps consumers find the best deals for fuel and it drives down prices.
“It must be independent of the Government, but the Scottish Government should help to get it established quickly.”
Mr Rennie then asked: “Will you commit to introducing a similar price checker scheme for motorists in Scotland?”
The question was posed as home secretary Priti Patel called on police to use tough new powers which include imprisonment to stop fuel protesters bringing gridlock to motorways and major A-routes across the UK.
A Home Office source told the Daily Mail: “Through our Police, Crime, Sentencing and Courts Act, we have given the police a wealth of powers to deal with disruptive and damaging protests, including imprisonment and unlimited fines for those blocking a highway – actions which inflict further pain on those affected by rising prices.
“The Home Secretary would encourage and support the police to make use of all the powers available to them. Forces need to move people on.”
The stance was supported by Downing Street, with a senior Government source telling The Times: “The Government has given the police a lot of powers to deal with this sort of stuff and we are looking to them to use it. We want to know what they are going to do about it.”
Some 12 people were arrested on Monday as dozens of campaigners calling for a cut in fuel duty targeted the M4 in South Wales and Somerset, and stretches of the M5 from Devon to Bristol.