A Monte Carlo (MC) study is made of the scattering function P(k) of the discrete Kratky-Porod (KP) wormlike ring as a function of the magnitude k of the scattering vector, and an approximate formula is also derived for P(k) of the continuous (original) KP ring in the Daniels approximation. It is found from MC results that the peak appearing in the reduced Kratky plot, which is characteristic of the KP ring, lowers continuously from the random-coil-ring limit to the rigid-ring limit with decreasing reduced contour length (increasing chain stiffness), and that the intramolecular topological constraint to keep the KP ring having the tivial knot lowers the peak. It is then shown that the formula in the first Daniels approximation may reproduce well the MC results except for very large k. A comparison is also made of the formula with literature data for ring atacic polystyrene in cyclohexane-d(12) near Theta.