Ariel Allen, 28, was a fifth grade teacher at Oak Grove Elementary.
Durham Sheriff's Department investigators say the victim was an 11-year-old student at the school.
The alleged incidents took place between March 1t and April 30.
They say the child told a parent and the parent called the sheriff.
A spokesperson for Durham Public Schools says Allen resigned from his teaching position in June.
Allen's attorney says he "vehemently denies all the allegations against him. Allen is innocent of all charges."