Actually, Jackie Robinson was the first modern African-American to play Major League Baseball, but he was not the first. He is credited with breaking the baseball color line since it had been a half century since a black man played Major League Baseball. Here is a line from a baseball almanac website:
05-01-1884 Moses Fleetwood Walker is the first black major league player and he goes 0-3 with Toledo of the American Association.
The answer to this question is Jackie Robinson. Jackie Robinson was the first African American to play for a Major League Baseball team. He made his debut with the Brooklyn Dodgers (who have since moved to Los Angeles) in April of 1947. During that year, and for some years afterwards, Robinson endured a great deal in the way of racist treatment from players on other teams and from fans. He was noted for being able to keep his temper while being treated in these ways. Robinson played for the Dodgers until he retired in 1956. He is now in the Baseball Hall of Fame and was named to the Major League Baseball All-Century Team.