We study the effects of bulge elongation on the star formation activity in the centers of spiral galaxies using the data from the Sloan Digital Sky Survey Data Release 7. We construct a volume-limited sample of face-on spiral galaxies with $M_r < -$19.5 mag at 0.02 $leq z <$ 0.055 by excluding barred galaxies, where the aperture of the SDSS spectroscopic fibre covers the bulges of the galaxies. We adopt the ellipticity of bulges measured by Simard et al. (2011) who performed two-dimensional bulge+disc decompositions using the SDSS images of galaxies, and identify nuclear starbursts using the fibre specific star formation rates derived from the SDSS spectra. We find a statistically significant correlation between bulge elongation and nuclear starbursts in the sense that the fraction of nuclear starbursts increases with bulge elongation. This correlation is more prominent for fainter and redder galaxies, which exhibit higher ratios of elongated bulges. We find no significant environmental dependence of the correlation between bulge elongation and nuclear starbursts. These results suggest that non-axisymmetric bulges can efficiently feed the gas into the centre of galaxies to trigger nuclear starburst activity.