A theoretical model of the nuclear spin isomer conversion in C$_2$H$_4$ induced by the intramolecular spin-spin interaction between hydrogen nuclei has been developed. In the ground electronic state, C$_2$H$_4$ has four nuclear spin isomers in contrast to two isomers in the molecules studied so far in this field of research. At the gas pressure 1 Torr, the rate of conversion between isomers with the nuclear spin symmetries $B_{1u}$ and $B_{2u}$ was found to be $5.2\times10^{-4}$~s$^{-1}$ which coincides within an experimental error with the rate recently measured by Sun, et al., Science, {\bf 310}, 1938 (2005). It was determined that at low gas pressures the conversion is induced mainly by the mixing of only one pair of rotational states. The calculated pressure dependence of the conversion rate predicts that conversion slows down with increasing pressure at pressures higher than 300 Torr.