Let f : C → C be a hyperbolic rational map of degree d ≥ 2, and let J ⊂ C be its Julia set. We prove that J always has positive Fourier dimension. The case where J is included in a circle follows from a recent work of Sahlsten and Stevens [SS20]. In the case where J is not included in a circle, we prove that a large family of probability measures supported on J exhibit polynomial Fourier decay: our result applies in particular to the measure of maximal entropy and to the conformal measure.