An exact solution is presented to a problem of spiralling self-avoiding walks on the square lattice recently proposed by Privman (1983). For N to infinity , the number of N-step spiral walks increases as c_N approximately=2^-23^-5/4 pi N^-7/4 exp(2 pi (N/3)^1/2), and their root-mean-square end-to-end distance behaves as R_N approximately=¹/₂ square root pi ^-1N^1/2 log N.