When released in North America, Rumble in the Bronx received generally good reviews, as most critics were happy that a Jackie Chan film was finally getting a wide theatrical release in North America. The film currently has a 78% approval rating on Rotten Tomatoes, and 81% among the 'Cream of the Crop.' Most critics agreed that the plot and acting were lacking, but the action, stunts, and Chan's charm made up for it.

Roger Ebert's review for the Chicago Sun-Times was:

"Any attempt to defend this movie on rational grounds is futile. Don't tell me about the plot and the dialogue. Don't dwell on the acting. The whole point is Jackie Chan - and, like Astaire and Rogers, he does what he does better than anybody. There is a physical confidence, a grace, an elegance to the way he moves. There is humor to the choreography of the fights (which are never too gruesome).He's having fun. If we allow ourselves to get in the right frame of mind, so are we.