Back in the early to mid 2000's Cartoon Network's website had a Dexter's Lab game which involved fighting robots, and as all of their games at that time involved scenes in their episodes there is an episode out there somewhere referencing BattleBots.
Scooby-Doo! Mask of the Blue Falcon
In a flashback, there is a scene depicting killer-robots, including a tournament. The film's main villain Jack Rabble was also a competitor and became a champion at least once, but was later permanently banished after installing one robot with rockets that went out of control and destroyed much of the building the event took place in.
Star Wars: The Clone Wars (film)
The protocol droid 4A-7 referred to the battle droids as "Battlebots" (twice in fact).
We Bare Bears
In the latest episode "Icy Nights", Ice Bear stumbles upon a killer-robot tournament while looking for his stolen Roomba (the thieves stole the Roomba just to compete). Ice Bear was even placed in the arena (while tied to a chair) and pitted against his own Roomba, and later both were mobbed by the rest of the robots. Ice Bear's Roomba got destroyed in the scuffle, but Ice Bear, enraged by this, destroyed all the other robots in retaliation.
Coincidentally the entire series of We Bare Bears itself also takes place in San Francisco, where BattleBots too was primarily hosted.
Malcom in the Middle
An episode of Malcom in the Middle features at least two BattleBots clips before Malcom and his family decide to build their own robot.
Big Hero 6
One of the scenes in the movie involves a robot fighting competition.
One of the comics features a direct call-out to Battlebots in the last panel.