Hunter Richard said he was the victim of an unprovoked assault when an unidentified man threw a drink in his face and snatched his red cap.
The 16-year-old filmed the incident, which took place at Whataburger in San Antonio on Tuesday night.
The man is heard in the clip saying the hat will look good in his fireplace.
Hunter told WOAI-TV: “I support my president and if you don’t let’s have a conversation about it instead of ripping my hat off.
“I just think a conversation about politics is more productive for the entire whole rather than taking my hat and yelling subjective words to me.”
US President Donald Trump’s son, Donald Trump Jr, shared the video on Twitter, calling it “disgusting”.
The San Antonio Police Department confirmed it was investigating the incident.
Investigators said the suspect was a 30-year-old man, but would not be identified unless a warrant was issued.
Whataburger Corporate Communications later said in a statement: “We were shocked to see this video and certainly don’t condone this type of customer behaviour in our restaurants.”
Rumble, a San Antonio bar, said on Facebook the attacker was one of its employees.
The bar said it had fired him because his alleged actions “go against everything that this establishment stands for”.
Rumble later deleted its Facebook page after a number of comments about the incident.
The red cap emblazoned with Mr Trump’s campaign slogan has become a trademark of his supporters.