Update 20/02: Le Havoc is now available in-game! Take the opportunity to go to the top 1!
Double the hop ups, double the fun! Here comes the Havoc: https://t.co/7pzKO4q7Ku pic.twitter.com/fFmJ3jASOX
— Apex Legends (@PlayApex) February 20, 2019
Update 15/02: Stats for a Havoc Rifle have been found in the game files, which seems to confirm its imminent arrival. The Havoc Rifle would be an assault rifle with energy ammunition, dealing between 18 and 36 damage.
As for how it looks, it could be the rifle held by Pathfinder in the Apex Legends intro cutscene.
Pathfinder carrying what appears to be the Havoc Rifle in the Apex Legends cutscene.
As the game continues to attract more and more players, Respawn has just rolled out a first patch on Apex Legends. However, this update (see the patch note in French) added lines of dialogue on several characters, including one on Bangalore which seems to indicate the arrival of a new weapon on the Battle Royale.
Indeed, when interacting with equipment and teammates, Bangalore responds "if you have a Havoc or a Prowler", a new line of dialogue since yesterday's patch.
Note that shampooh (source in English), a dataminer known by the Titanfall 2 community, found some elements on the game files concerning the weapon, which would have a full auto mode. Also, the Havoc could charge a powerful shot on its secondary mode.
It now remains to be seen when Respawn intends to add this new weapon to Apex Legends.
The list of Legends of Apex Legends