Jones, who kicked collegiately at Tulsa, had not previously been on an NFL roster; his final college game was in November 2017.
He now has a chance to compete for the starting job with Parkey, who missed a field goal at the end of an NFC wild-card round game against the Philadelphia Eagles that would have won it for Chicago. Parkey struggled in his first season with the Bears, missing a total of 11 kicks, the most by any kicker in the league.
The Bears worked out five other kickers Friday in addition to Jones: former Jets kicker Nick Folk, Josh Gable, Ernesto Lacayo, Austin MacGinnis and Blair Walsh.
Chicago signed Parkey in free agency to a contract that included $9 million in guaranteed money, but Parkey missed eight field goals and three extra points for the Bears, including the ill-fated, last-second field goal attempt against the Eagles that bounced off the left upright and hit the crossbar. The NFL later credited Philadelphia with a blocked field goal after slow-motion replays revealed that Parkey's kick was slightly tipped at the line of scrimmage.
He bounced four kicks off the uprights during a Week 10 victory over the Detroit Lions.
The team would have to carry $4,437,500 worth of dead salary-cap money if it cuts Parkey.
Head coach Matt Nagy expressed disapproval last week with Parkey's decision to appear as a guest on "The Today Show" five days after missing his final attempt against Philadelphia.
On Wednesday, quarterback Mitchell Trubisky said he supported Parkey regardless of his decision to go on TV.
"He made a personal decision, and us being teammates and a family, we've just got to support our guys no matter what they do," Trubisky said.
When asked about Parkey last week, general manager Ryan Pace said: "I know Cody wishes he had a better season. We wish he had a better season, too. We've just got to evaluate that now. You've got to be honest with yourselves in these. I think as we go forward, that's when we've got to be real and say, hey, that's an important position for us. It's a position of emphasis."
At the minimum, Pace said the Bears will have a kicker competition in 2019, if not an outright change.
"That's going to be an emphasis and focus for us, the kicker position, and there'll definitely be competition there," Pace said.
For now, the competition starts with Jones.
Information from ESPN's Jeff Dickerson was used in this report.