We present the optical transmission spectrum of the highly inflated Saturn- mass exoplanet WASP-21b, using three transits obtained with the ACAM instrument on the William Herschel Telescope through the LRG-BEASTS survey (Low Resolution Ground-Based Exoplanet Atmosphere Survey using Transmission Spectroscopy). Our transmission spectrum covers a wavelength range of 4635-9000{AA}, achieving an average transit depth precision of 197ppm compared to one atmospheric scale height at 246ppm. We detect NaI absorption in a bin width of 30{AA}, at >4{sigma} confidence, which extends over 100{AA}. We see no evidence of absorption from KI. Atmospheric retrieval analysis of the scattering slope indicates it is too steep for Rayleigh scattering from H_2, but is very similar to that of HD 189733b. The features observed in our transmission spectrum cannot be caused by stellar activity alone, with photometric monitoring of WASP-21 showing it to be an inactive star. We therefore conclude that aerosols in the atmosphere of WASP-21b are giving rise to the steep slope that we observe, and that WASP-21b is an excellent target for infra-red observations to constrain its atmospheric metallicity.