Ichiro Suzuki won the 2001 AL batting title with a .350 mark, and was less than .0004 behind Larry Walker for the overall MLB lead (Walker .35010, Suzuki .34971 -- both recorded as .350).
A few others have led their league in their first full season, but had played a partial season previously; and there were a few who won outright in their first season, back in the 19th century. The two most recent were:
Wade Boggs, 1983 Boston Red Sox, .361 (led majors) -- played 104 games in 1982 (which qualified as his rookie season).
Pete Reiser, 1941 Brooklyn Dodgers, .343 (trailed three AL players -- Williams' famous .406, Travis, and DiMaggio) -- played 58 games in 1940 (which would have qualified as his rookie season under current guidelines).
NL rookie mark -- .373, George Watkins, 1930 St. Louis Cardinals.
AL rookie mark -- .350, Ichiro Suzuki, 2001 Seattle Mariners.