Corey Curtis, 31, from Grays Ferry, turned himself in Friday.
He was charged with attempted murder, aggravated assault, and other related offenses.
The shooting happened Thursday just before 2 p.m. on the 1700 block of Chestnut Street.
Police said the incident began when Curtis, the driver of a white car, pulled into a parking spot near the intersection of 17th and Chestnut streets that a food delivery driver wanted to park in, too.
The delivery driver allegedly got out of his silver SUV, and the two exchanged words.
That's when the delivery driver punched Curtis, knocking him off his feet, police said. Curtis then shot the delivery driver in the jaw and back.
Dispute over parking space led to Center City Philadelphia shooting: Police
The delivery driver tried to drive off, but he didn't make it far. Police say he got to the intersection of 17th and Chesnut streets because he could barely drive.
A good Samaritan then took the delivery driver to Thomas Jefferson University Hospital where he was listed in critical condition.
Police are thankful no one else was injured.
"In a situation like this, he hit his intended target, but think about how many people out here with them bullets flying," said Captain John Walker.
Anyone with information is asked to call police at 215-686-TIPS.