Yes, you can encounter and catch the shiny version of Rayquaza in Pokemon GO, although, like all other shiny Pokemon, it is very rare.
After beating a Rayquaza or Mega Rayquaza Raid, there is a low chance of the Rayquaza you encounter after being a shiny version of this Legendary.
How to Get Shiny Rayquaza in Pokemon GO
The only way to encounter Rayquaza in Pokemon GO is by winning either a Rayquaza or Mega Rayquaza Raid. Then, you need to hope that the Rayquaza you encounter as a reward is shiny.
Unfortunately, there is no way to guarantee finding a shiny Rayquaza or even boost the odds of it being shiny.

Rayquaza Shiny Odds
The odds of Rayquaza being shiny in Pokemon GO are 5%, or 1 in 20 – the standard shiny odds for Legendary Pokemon in Pokemon GO.
Therefore, on average, you’ll need to encounter Rayquaza 20 times before you find the shiny version!
What Color is Shiny Rayquaza in Pokemon GO?
The shiny version of Rayquaza is a charcoal-black color instead of green, but the details remain the same color as the normal version. The shiny version still has yellow markings and pink edges on its fins.
This striking black and yellow color scheme makes shiny Rayquaza one of the most sought-after shinies in the whole game!
