We present an optical transmission spectrum for WASP-94A b, the first atmospheric characterization of this highly-inflated hot Jupiter. The planet has a reported radius of 1.72^+0.06^-0.05_R_Jup, a mass of only 0.456^+0.032^-0.036_M_Jup, and an equilibrium temperature of 1508+/-75K. We observed the planet transit spectroscopically with the EFOSC2 instrument on the ESO New Technology Telescope (NTT) at La Silla, Chile: the first use of NTT/EFOSC2 for transmission spectroscopy. We achieved an average transit-depth precision of 128ppm for bin widths of ~200{AA}. This high precision was achieved in part by linking Gaussian Process hyperparameters across all wavelength bins. The resulting transmission spectrum, spanning a wavelength range of 3800-7140{AA}, exhibits a sodium absorption with a significance of 4.9{sigma}, suggesting a relatively cloud-free atmosphere. The sodium signal may be broadened, with a best-fitting width of 78^+67^-32{AA} in contrast to the instrumental resolution of 27.2+/-0.2{AA}. We also detect a steep slope in the blue end of the transmission spectrum, indicating the presence of Rayleigh scattering in the atmosphere of WASP-94A b. Retrieval models show evidence for the observed slope to be super-Rayleigh and potential causes are discussed. Finally, we find narrow absorption cores in the CaII H&K lines of WASP-94A, suggesting the star is enshrouded in gas escaping the hot Jupiter.