Group leader Councillor Thomas Kerr is urging the administration to ditch their policy that was introduced just a week ago.
The petition highlights that the city is in the midst of a cleansing crisis, and believes this charge will do nothing to solve the problem.
Councillor Kerr is concerned it could create a two-tier system between car owners and non-drivers or those on low incomes.
He said: “This is yet another reckless move by an already out of touch council.
“The introduction of the bulk uplift charge last week will do nothing to fix Glasgow’s cleansing crisis.
“Instead, it risks exacerbating the problem as well as penalising those on low incomes and likely lead to even more fly-tipping over the city.
“That is why we have launched our campaign to reverse this charge immediately. We have fought this policy at every stage and had fully costed plans that would have scrapped this move, but other parties couldn’t bring themselves to support us.
“We urge people from across Glasgow to stand with us, sign the petition and call on the council to think again.
"We won’t be giving up, and are completely committed to clean up the mess that the administration in this city has created.”
The council previously pointed out charging to collect bulky items is standard practice in almost every other local authority area in Scotland.
A spokesman said: “The decision to introduce charging for bulky items was democratically agreed at a full council meeting in February 2020.
“The vast majority of people will always dispose of their waste responsibly and we are trying to encourage greater re-use and recycling of unwanted items.
“Reducing the amount of waste we produce as a city is good for the environment as it helps reduce our carbon footprint, which is essential if we are to tackle the climate emergency.
“People can dispose of their large, unwanted items at our waste centres free of charge while the vast majority of the city’s housing associations now also collect large items of behalf of their tenants.”
To sign the petition visit www.glasgowconservatives.org.uk/form/bulk-uplift-survey