The video, which made rounds on social media, shows a man police say is Andre Robinson, 21, gently coaxing the animal towards him, then violently kicking it several feet in the air.
Robinson was arrested later that day and charged with aggravated cruelty to animals, police said.
The cat has not been located, police said.
An online petition to prosecute Robinson went up shortly after the video went viral. More than 4,000 people have signed the petition as of Tuesday morning.
Robinson has two previous arrests, including a 2011 arrest for after allegedly stealing an iPhone at knifepoint, police said. He also has six sealed arrests, according to the Daily News.