According to the school, Shannon Jr. turned himself in to police in Douglas County, Kansas, on a warrant for his arrest this week ... after he was accused of sexual misconduct while he was in Lawrence back in September for Illinois' football game against the Jayhawks.

The school said Shannon Jr. was "not in Lawrence on official University business, nor was he a member of the University's travel party" when the alleged incident happened.

Jail records show Shannon Jr. posted $50,000 bail shortly after cops placed him in custody on Thursday.

The basketball player's attorney, Mark P. Sutter, said in a statement his client is innocent ... writing, "Since September, when these allegations surfaced, Terrence has cooperated with law enforcement throughout the investigation, declaring his innocence from the beginning."

"Now, several months later, my office learned that formal charges were filed against him yesterday in Lawrence, KS," Sutter added. "In less than 24 hours, my client responded, and he voluntarily surrendered to local authorities for processing and release. Terrence is innocent of these charges, and he intends to take his case to trial."

Shannon Jr. just transferred to Illinois last season after three years at Texas Tech -- and he's become the Illini's best player.