Halo Infinite does not currently have a battle royale mode, but it appears that will soon change.
In a recent tweet, Certain Affinity, a studio that specializes in multiplayer components for shooters like Call of Duty, Halo, and DOOM, confirmed that 343 Industries had entrusted it "with further evolving Halo Infinite in some new and exciting ways." If you follow the page linked to by the tweet (embedded below), you'll see Certain Affinity's careers page, which now has dozens of open positions. The tweet might just be the company's attempt to recruit talent, but some players are convinced that it's for a big battle royale mode for Halo Infinite.
After bursting into the scene in 2017, battle royale has been at the forefront of the video game industry. Industry giants like Call of Duty and Battlefield couldn't help but jump on the bandwagon. It only makes sense for Halo to do so with Halo Infinite.
Unfortunately, we have no idea what Certain Affinity's take on battle royale would look like and if it is even in the works. A previous report from Windows Central suggests that the in-development battle royale mode, Tatanka, is going to be more "newcomer-friendly" when compared to Halo Infinite's standard selection of game modes. It's also not known if this is related to Big Team Battle: Last Spartan Standing, which was first announced back in March along with Season 2.