Rayquaza can viably run both mixed (having both physical and special moves and the required stats) and physical sets in Gen 3 Ubers. Fully special Rayquaza is rarely ever seen, though.
The physical sets include Choice Band (most common) and Dragon Dance (rarer comparatively).
It can also viably run a mixed set with BoltBeam coverage, Extreme Speed and a filler move (one of Brick Break, Fire Blast or Rock Slide).
List of Common Movesets:
Choice Band
Rayquaza @ Choice Band
Ability: Air Lock
EVs: 40 HP / 252 Atk / 216 Spe
Adamant Nature
- Double Edge
- Earthquake
- Extreme Speed
- Rock Slide / Overheat
Mixed
Rayquaza @ Lum Berry / Never-Melt Ice
Ability: Air Lock
EVs: 40 Atk / 252 SpA / 216 Spe
Mild Nature
- Ice Beam
- Thunderbolt
- Extreme Speed
- Brick Break / Fire Blast / Rock Slide
Dragon Dance
Rayquaza @ Sharp Beak / Silk Scarf
Ability: Air Lock
EVs: 40 HP / 252 Atk / 216 Spe
Adamant Nature
- Dragon Dance
- Hidden Power Flying / Double Edge
- Earthquake
- Extreme Speed
Source
Note: I'd normally link an analysis, but the one for Rayquaza in Gen 3 is outdated.