  The Galactic interstellar turbulence affects the density distribution and
star formation. We introduce a new method of measuring interstellar turbulent
density spectra by using the dispersion measures (DMs) of a large sample of
pulsars. Without the need of invoking multiple tracers, we obtain nonuniversal
density spectra in the multi-phase interstellar medium over different ranges of
length scales. By comparing the analytical structure function of DMs with the
observationally measured one in different areas of sky, we find a shallow
density spectrum arising from the supersonic turbulence in cold interstellar
phases, and a Kolmogorov-like density spectrum in the diffuse warm ionized
medium (WIM). Both spectra extend up to hundreds of pc. On larger scales, we
for the first time identify a steep density spectrum in the diffuse WIM
extending up to several kpc. Our results show that the DMs of pulsars can
provide unique new information on the interstellar turbulence.
