A short cut to getting that vibe would be a high baffled mouthpiece and learning to growl.
But that barely puts you in the ball park really.
Seek and you'll find that the big man had a big tone behind the rock guise he put on it.
Which came from hours and hours and more hours of all the exercises every sax player should do more of.
Long tones, overtones, scales, etc
Basically dedicated practise.