Galveston Police apologised last year after footage emerged of Donald Neely, 44, arrested for criminal trespassing.
A lawsuit filed this week alleged the officers' conduct was "extreme and outrageous" and caused Mr Neely injury and emotional and mental anguish.
The trespass charges against Mr Neely were later dismissed in court.
Many people on social media compared the footage of Mr Neely to the slavery era, an allusion referenced explicitly in the lawsuit. According to the lawsuit, the officers should have been aware that Mr Neely, "being led with a rope and by mounted officers down a city street as though he was a slave, would find this contact offensive".
Accusing both the city and the Galveston police department of negligence, the suit says that Mr Neely "suffered from handcuff abrasions, suffered from the heat, and suffered from embarrassment, humiliation and fear".
City officials declined to comment on the lawsuit to US media.
Last year, after an outcry over images of Mr Neely, police clarified that he was not tied with the rope but was "handcuffed and a line was clipped to the handcuffs".
Galveston's police chief Vernon Hale said at the time that the technique was acceptable in some scenarios but that "officers showed poor judgment in this instance".
There was no "malicious intent", he said, and apologised to Mr Neely for the "unnecessary embarrassment". Department policy was changed to prevent the use of this technique.
Mr Neely - who was homeless at the time - was sleeping on a sidewalk, US media reported, when he was arrested for criminal trespass and led around the block to a mounted police patrol staging area. The charges were later dismissed.
Following an investigation into the encounter, the department released body camera footage of the arrest. In it, the officers can be heard commenting on the appearance of Mr Neely's arrest.
"This is going to look so bad. I'm glad you're not embarrassed, Mr Neely," one officer is heard saying.
A status conference is currently scheduled for 7 January, 2021. Mr Neely is requesting a trial by jury, according to court documents.