We study the phase diagram of N f = 2 + 1 QCD in the T − µB plane and investigate the critical point corresponding to the onset of the Roberge-Weiss transition, which is found for imaginary values of µB. We make use of stout improved staggered fermions and of the tree level Symanzik gauge action, and explore four different sets of lattice spacings, corresponding to Nt = 4, 6, 8, 10, and different spatial sizes, in order to assess the universality class of the critical point. The continuum extrapolated value of the endpoint temperature is found to be TRW = 208(5) MeV, i.e. TRW/Tc ∼ 1.34 (7), where Tc is the chiral pseudocritical temperature at zero chemical potential, while our finite size scaling analysis, performed on Nt = 4 and Nt = 6 lattices, provides evidence for a critical point in the 3d Ising universality class.