HOUSTON — The Texas state trooper who arrested Sandra Bland, the black woman who was found hanging in a Waller County jail cell in 2015 and whose death became a symbol of the national debate over the treatment of blacks by the police, was cleared on Wednesday of the only criminal charge he faced in the case.

The trooper, Brian T. Encinia, was indicted last year by a Waller County grand jury on a perjury charge, in connection with his description of the arrest of Ms. Bland, whom he pulled over in July 2015 in a routine traffic stop in Prairie View, northwest of Houston. On Wednesday, the perjury charge against Mr. Encinia was dismissed by a judge, after prosecutors filed a motion asking for the charge to be dropped.

The charge, a misdemeanor, led to Mr. Encinia’s firing by the Texas Department of Public Safety. He had fought the charge, pleading not guilty. The same grand jury that indicted Mr. Encinia had declined to indict any of Ms. Bland’s jailers in connection with her death, which the medical examiner had ruled a suicide.

Ms. Bland, 28, of Chicago, was returning to Texas to take a job at Prairie View A&M University, her alma mater, when Mr. Encinia pulled her over for failing to use her turn signal. A dashboard-camera video of the episode captured Mr. Encinia’s tense encounter with Ms. Bland, showing him threatening her with a Taser and arresting her on a charge of assaulting a public servant.