The workout is thought to be Jones' first with an NFL team since the Cowboys released him in February 2009.
Bengals coach Marvin Lewis has been a champion in providing second chances to players.
Jones has avoided trouble since his last brush with the law in October 2008. He was involved in an alcohol-related incident with a bodyguard assigned to him by the Cowboys, and hotel employees called police. No arrests were made nor charges filed. But the NFL suspended Jones for four games because the incident was a violation of the league's personal conduct policy.
Jones began his time in Dallas under close league scrutiny after he was suspended for the entire 2007 season for multiple violations of the conduct policy while he was a member of the Titans. The Cowboys traded for Jones before his suspension was over and he was reinstated by NFL commissioner Roger Goodell on Aug. 28, 2008.
The Bengals, who earlier had expressed interest in former Jaguars receiver Matt Jones, signed him to a one-year contract Friday. According to the Cincinnati Enquirer, the deal is worth about $700,000.
Jones had been suspended for the final three games of the 2008 season for violating the league's substance abuse policy. He was cut by the Jaguars in March 2009.
Adam Schefter is ESPN's NFL Insider.