On the same day that Rise of the Tomb Raider was launched on PC, Amazon.com opened the pre-orders of Crystal Dynamics' game on PlayStation 4. The launch date on the game's product page is set for December 30, 2016, but that is surely a placeholder
It's more plausible that the plans regarding the launch date for Rise of the Tomb Raider on Sony's console will be revealed in the coming months, in late spring or during the summer (maybe during E3 in Los Angeles?). At the moment, the only thing we know is that the game will be available on PS4 but not before the next Christmas period. The most likely scenario is that Microsoft secured 12 months of exclusivity meaning the game can go on sale on PS4 in November of this year.