The question can be answered compellingly either way. The Chorus declares that Romeo and Juliet were "star-cross'd". Romeo refers to "some consequence yet hanging in the stars". After he kills Tybalt, he cries, "O I am Fortune's fool!" One can talk forever about the number of coincidences in the play.
However, the characters' own actions must account tor the tragedy, to a large extent. Romeo, in particular, is very impetuous, and his rash decisions (his quick change of heart about Rosaline, his determination to marry Juliet immediately, and his killing of Tybalt) have terrible consequences.
In the classical sense, there is no such thing as a tragedy of fate. Tragedy is the result of the choices of the characters in the play, the product of their personality flaws. But nowadays we take a more liberal view, and think of "tragedy" as any sad death, regardless of its cause or stature. However you answer this question, you will have plenty of evidence from the text to support your opinion.