The pretrial intervention program is a diversion program that permits certain defendants (particularly first-time ones) to avoid formal prosecution.
If Rice is not approved for the program, his next court date is scheduled for May 29. Prosecutors have offered a plea agreement in which Rice would receive probation with no jail time and undergo anger-management counseling.
Rice was arrested and charged with simple assault-domestic violence on Feb. 15 after a physical altercation with his then-fiancée, Janay Palmer, at the Revel Casino and Hotel in Atlantic City, New Jersey. Palmer also was charged in the incident.
Rice was indicted by a grand jury in late March for allegedly striking Palmer. The two were married one day later, and Palmer was seated behind Rice in the courtroom Thursday.
The former Rutgers star arrived at the courthouse holding hands with Palmer. He said he is a "happy father and a happy husband." When reporters asked what he hoped would happen, Rice responded, "for you all to have a blessed day."
Even if Rice avoids being convicted, he likely will receive punishment from the NFL, whether it's a fine or suspension, under the league's personal conduct policy.
On Wednesday, Ravens general manager Ozzie Newsome said the uncertainty surrounding Rice's future won't affect the team's draft plans.
"We'll deal with Ray when that time comes," Newsome said at the Ravens' pre-draft news conference, adding that the team was talking about adding one or two running backs even before Rice's incident.
The Associated Press contributed to this report.