Williams started a "Small Amount of Marijuana" program that requires offenders to attend a three-hour drug abuse class and pay a $200 fine - a move aimed at sweeping 3,000 marijuana cases annually out of the main court system.
"If the D.A. is not going to prosecute . . . then there's no reason to arrest," Kenney said.
Rather, his bill would allow officers to issue a summons, similar to a traffic ticket, requiring people caught with a small amount of marijuana to appear in the special program.
Kenney said the change would free up 17,000 police hours spent processing people arrested for pot possession.
He also noted that an arrest is "traumatic" and that those nabbed for pot possession in Philadelphia are disproportionately African American - 89 percent in 2012, according to his data.
"God forbid, the kid bolts and they end up Tasing him and he gets hurt, and the cop turns an ankle and he gets hurt - all for something we're not prosecuting," Kenney said.
The bill comes amid a small but growing legalization and decriminalization trend in the United States. Most recently, Colorado legalized recreational marijuana use, and President Obama told the New Yorker magazine he considered pot "a bad habit and a vice" no more dangerous than drinking - though he did not endorse legalization.
Last year, the City of Chicago approved a bill similar to Kenney's that made the penalty of pot possession a fine. Washington's city council is debating a bill that would drop the penalty to a fine as low as $25.
Kenney, a potential mayoral candidate in 2015, described his proposal as a "smart and reasonable measure" that would make better use of limited law enforcement resources.
A spokeswoman for the District Attorney's Office, which closed early Tuesday for the snowstorm, could not immediately provide a comment on Kenney's bill.
As for eventual legalization of marijuana, Kenney said he was "up in the air on that."
"I need to do more research on that," he said. "But the war on drugs hasn't worked."