People living in Lumby's Terrace, off Water Street, say they are sick and tired of cars speeding along their road as a shortcut off Barnack Road.
They want the road to be made uphill-only from Water Street.
Derrick Middleton, 66, of Lumby's Terrace, fears the road is "an accident waiting to happen". He said: "This is an area that needs to be made safe for children and the pupils at Stamford High School. At the moment it's simply too dangerous."
The petition will be handed to Stamford Town Council and Lincolnshire County Council, which controls road policy.
The residents hope their petition forces a change but are prepared to push for even tighter measures if necessary.
Another proposal they are considering is to demand bollards be installed at the top of Lumby's Terrace to deter drivers coming downhill from Barnack Road.
Lumby's Terrace resident Josie Clarkson, 67, said the road was being used as a rat-run.
"I have almost been run over as there's a blind spot between a house and a wall and cars coming downhill can't see people walking up," she said.
Stamford town councillor Harrish Bisnauthsing (Lib Dem)
is supporting the residents' campaign.
"People shoot down at high speed, using it as a cut-through and this is a problem which needs to be addressed," he said.
A Lincolnshire County Council spokesman said the authority would welcome residents' views.
He said: "When a petition is received it is acknowledged by the relevant officer and will then be presented to councillors for consideration at the next meeting of the planning and regulation committee."