Mr Chauvin was arrested and charged with third-degree murder and manslaughter on Friday, but protests that initially started in Minneapolis last week spread to Los Angeles and New York City, among other cities in the US over the weekend.
Mr Cotton, a senator for Arkansas, blamed “anarchists” for trouble at protests, and told Fox News that greater force needs to be employed.
He said: “If local politicians will not do their most basic job to protect our citizens, let’s see how these anarchists respond when the 101st Airborne is on the other side of the street.”
The 101st Airborne Division of the US Army is a specialised unit of the armed forces that consists of around 29,000 troops trained for air assault operations.
The division uses helicopters to deliver its troops into combat and has fought in multiple wars and battles over the last 100 years.
They last deployed soldiers in Somalia, but have had troops fight during WWI, the Vietnam war and in Afghanistan and Iraq in the last 20 years. It famously took part in the D-Day landings and the Battle of the Bulge, with its exploits dramatised in the TV series Band of Brothers.
Footage has shown police in different cities in the US using excessive force, including an incident in New York City, where a police car drove into a group of protesters.
There has also been footage released of a minority of protesters attacking police vehicles and shops, which president Donald Trump claimed was carried out by anarchists and anti-facist group Antifa.
He tweeted: “It’s ANTIFA and the Radical Left. Don’t lay the blame on others!”
His comments were echoed by attorney general William Barr, who said: “The violence instigated and carried out by Antifa and other similar groups in connection with the rioting is domestic terrorism and will be treated accordingly.”
In a later tweet, Mr Cotton reiterated his stance and said that the US needs to have “zero tolerance” for violence during the protests.
“Anarchy, rioting, and looting needs to end tonight. If local law enforcement is overwhelmed and needs backup, let’s see how tough these Antifa terrorists are when they’re facing off with the 101st Airborne Division,” he said.
“We need to have zero tolerance for this destruction.”