Another possibility:
1991 Face to Face: The Famous Celebrity Guessing Game Cards - Numbered #280 - George Steinbrenner
Courtesy of COMC.com
I see the list above, and due to the nature of these sets, I would say NONE of these are "rookie cards." Only one even has his name on it, and they're all from oddball sets (or my link is from a board game) with mostly cartoon drawings. If you're asking which would PSA count for their Set Registry HOF Rookie Cards, I would guess none of these.
They'd probably use whichever company out of Topps or Panini created the first mass-produced RC, likely the Panini Cooperstown base card, as long as it was licensed by Steinbrenner's family. It's pretty shocking that he doesn't have any true baseball cards (Topps, UD, Fleer, Panini, Donruss, etc) over the years, nor any Yankee Team Issues that I can find.