Rayquaza is a Generation 3 member of the Weather Trio. It is a very good and highest quality wild Pokémon in Ruby. Now you can get your hands on it.
Steps

Step 1. To get to the “Sky Pillar”, you must first defeat the elite four and the champion
Also, you must have a “Mach Bike” and a Pokémon that knows the “Surf” movement. But considering that you have defeated the Pokémon League, this should not be difficult for you.

Step 2. To quickly get to the “Sky Column”, you need to fly to “Pacifidlog Town”, then slide to the right
If you stick to the top of your path, you will see that it turns left after a while. Take two or three turns and you will reach a small island. Enter the cave and head up the stairs. This will take you to the Heavenly Column.

Step 3. You may need “Repels”, but not required
To go through the first floor, move clockwise around the center.

Step 4. On the second floor, you will see cracked tiles
You must drive the Mach Bike at full speed or you will fail. Remember to save your game before going through the cracked tiles. To get to the third floor, move clockwise around the center at maximum speed.

Step 5. When you get to the third floor, you will notice a door on the right
It will be available at a later date. Now move counterclockwise up the steps.

Step 6. On the fourth floor, use the Mach Bike again and move clockwise
You will reach a passage to the next staircase, which will be blocked by stones. This is where it gets tricky. Use Mach Bike and stop in the middle of the cracked tile. If you fall through the nearest and farthest tiles, you will have to go through the third and fourth floors again. Step 7. Once you have fallen down, move to the nearest stairs, as indicated earlier.
Now, on the fourth floor, another staircase will be available to you. There are no cracked tiles on the fifth floor, so you can walk, run, or ride the Mach Bike counterclockwise and up the stairs.

Step 8. You are now at the top of the "Sky Column" where Rayquaza is waiting for you
It is very important to save the game at this point! Because if you miss Rayquaza, or something goes wrong, after restarting the game, you can start from the same place.

Step 9. After saving, go to Rayquaza and press “A” in order to start the fight
Rayquaza is level 70, so get ready for a tough fight.

Step 10. To make it easier for you to catch Rayquaza, freeze it at the beginning of the fight by using “False Swipe” several times until you have 1 HP left
Also use the “Confuse Ray” action to confuse him and increase the chance of being caught even more. Once you manage to freeze him, confuse him and leave one HP, use “Ultra” and / or “Timer Balls” until you catch him. This may take a while, so please be patient.
Advice
- Don't get too upset. You don't want to break your GBA / DS.
- If you have a Master Ball, you can use it in this case, or save it to capture another Legendary Pokemon.