Videos posted online show the BMW convertible slowly making its way down the long, wide staircase at about midnight Thursday before speeding off.
Photographer HughE Dillon runs the local entertainment website PhillyChitChat.com and lives nearby. He posted one of the videos online.
The district attorney's office says the car caused about $8,000 in damage to the steps and prosecutors have approved a felony charge of criminal mischief against the driver.
Police say they won't charge the driver until they can determine if a mechanical problem was to blame.
The driver's name hasn't been released.
The steps have become a popular tourist attraction since Sylvester Stallone run up them in "Rocky."