By creating a "smoke curtain" they hope to impede visibility from warplanes that have been carrying out bombing raids.
Rebel-held parts of Aleppo have been heavily bombarded recently by pro-government forces. Rebels have launched an offensive to try to break a government siege.
Russia is a key backer of Syrian President Bashar al-Assad and is supporting pro-government forces with air strikes. Government forces cut off rebel-held eastern parts of Aleppo last month.
Rami Jarrah, a journalist covering events in Syria, says the burning tyres are effective. "It's causing confusion for the jets and a diversion for the offensive on the ground that aims to break the siege.
"Everyone is doing it but to participate in the resistance this is really the only thing the children can do."
They are promoting a series of hashtags on Twitter to try to build momentum including #AngerForAleppo and #AleppoUnderSiege.
Aid organisations believe about 250,00 civilians still live in the rebel-controlled areas of Aleppo.
On Monday rebel fighters shot down a Russian helicopter killing all five on board.
The aircraft was returning from delivering humanitarian aid to the besieged city of Aleppo, Russian officials said.
It is not clear which group brought the helicopter down.
Children in the Syrian city of Aleppo are burning tyres in an attempt to create a no-fly zone above the besieged city.