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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 Å, achieving an average transit depth precision of 197 ppm compared to one atmospheric scale height at 246 ppm. We detect Na i absorption in a bin width of 30 Å  at >4σ confidence, which extends over 100 Å. We see no evidence of absorption from K i. Atmospheric retrieval analysis of the scattering slope indicates it is too steep for Rayleigh scattering from H2, 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 infrared observations to constrain its atmospheric metallicity.