In Romeo and Juliet, Romeo's fatalistic nature is established early in the first act when he expresses his misgivings about going to the Capulet fete:
I fear too early. For my mind misgives
Some consequence, yet hanging in the stars,
Shall bitterly begin his fearful date
With this night's revels, and expire the term
Of a despised life closed in my breast...(1.4.113-117)
So, analyzing Romeo's remarks in the context of his character and not just the statement of the moment, which will provide more insight, the reader discerns that Romeo is haunted by his previous forebodings and now understands that the "fearful date" of the stars has come; consequently, he realizes that he is a "fool" since he has earlier sensed the ominous presence of Fate, and, acting rashly and with effeminency--as he accuses himself--he has allowed himself to meet its "date."
What Romeo means when he says this is that his life is being completely controlled (and messed up) by fate (or fortune). He is being sad because his life has been turned upside down by a couple of twists of fate -- things that are not his fault, at least in his opinion.
Right at this point, what he means is that it was just bad luck that he has ended up killing Tybalt. He was trying to keep the peace but when Tybalt killed Mercutio, he lost control. Now he will surely be exiled or even executed because of the Prince's edict against fighting.
So this is why he is fortune's fool. He goes to break up a fight (because of his love for Juliet) and now he ends up killing Tybalt and getting himself in huge trouble (that will end up killing him and Juliet).