One. Well, not even that many, really. All you need to do is get into a game, which happens when your name is announced, even if you then get immediately removed (a second pinch-hitter, perhaps). Check out the major league stats of Larry Yount sometime.
A player is considered a rookie in every major league season up to and including the season in which his career major league numbers exceed either:
a. 130 at-bats, or
b. 50.0 innings pitched, or
c. 45 days on the active, 25-man roster (Opening Day through August 31).
"Rookie status" is essentially meaningless except for Rookie of the Year Award eligibility (and even then, the voters sometimes get it wrong).