Over the course of his long European soccer career, Zlatan Ibrahimovic has been accused of many things: being too moody, playing selfishly, looking like a pirate. Being a lucky charm isn't on the list.

But as his current side, A.C. Milan, battles for an Italian league title—it trails Juventus by a point with six games left—Ibrahimovic has a chance to extend a remarkable streak: For the last eight years, whichever team he has played for has won its league.

Since...