The Police Department is putting up $2,500 of the reward money with the Fraternal Order of Police putting up the remaining $5,000.
In Holmesburg earlier, Ramsey had raised the possibility of posting a reward to shake loose information.
"Somebody knows something," Ramsey said. "These things don't happen and it's kept totally quiet. There's some idiot somewhere bragging about it."
The commissioner said police had stepped up patrols in the area and residents had been very cooperative, even launching citizens patrols.
"Apparently that's not enough," he said, adding later, "that doesn't mean we give up."
Noting it can cost $500 to $600 to replace a set of tires, Ramsey said: "Who can afford to have this happen? I certainly couldn't. Who can do that over and over again?"
"Once [the vandals are] caught - and we will catch them - not only do they need to do serious jail time, they need to pay restitution."
"It just makes no sense at all and we've got to do something to stop it," the commissioner said.
The latest vandalism was discovered early today on the 4000 blocks of Aldine and Teasdale Streets in the Holmesburg section.
In the Northeast, tires on 55 vehicles have been slashed in five separate incidents, police said.
On Friday, owners of 11 cars awoke to find their tires had been slashed in Kensington, which is in the Police Department's East Division.