With an aim of getting information on the equatorial rotation velocity (v_e) of Sirius A separated from the inclination effect (sin i), a detailed profile analysis based on the Fourier transform technique was carried out for a large number of spectral lines, while explicitly taking into account the line-by-line differences in the centre-limb behaviours and the gravity darkening effect (which depend on the physical properties of each line) based on model calculations. The simulations showed that how the 1st-zero frequencies (q_1) of Fourier transform amplitudes depends on v_e is essentially determined by the temperature-sensitivity parameter (K) differing from line to line, and that Fe I lines (especially those of very weak ones) are more sensitive to v_e than Fe II lines. The following conclusions were drawn by comparing the theoretical and observed q_1 values for many Fe I and Fe II lines: (1) The projected rotational velocity (vsini) for Sirius A is fairly well established at 16.3 (+/-0.1) km/s by requiring that both Fe I and Fe II lines yield consistent results. (2) Although precise separation of v_e and i is difficult, v_e is concluded to be in the range of 16 < v_e < 30-40 km/s, which corresponds to 25 < i(deg) < 90. Accordingly, Sirius A is an intrinsically slow rotator for an A-type star, being consistent with its surface chemical peculiarity.