The evidence for benzonitrile (C$_6$H$_5$CN}) in the starless cloud core TMC-1 makes high-resolution studies of other aromatic nitriles and their ring-chain derivatives especially timely. One such species is phenylpropiolonitrile (3-phenyl-2-propynenitrile, C$_6$H$_5$C$_3$N), whose spectroscopic characterization is reported here for the first time. The low resolution (0.5 cm$^{-1}$) vibrational spectrum of C$_6$H$_5$C$_3$N} has been recorded at far- and mid-infrared wavelengths (50 - 3500 cm$^{-1}$) using a Fourier Transform interferometer, allowing for the assignment of band centers of 14 fundamental vibrational bands. The pure rotational spectrum of the species has been investigated using a chirped-pulse Fourier transform microwave (FTMW) spectrometer (6 - 18 GHz), a cavity enhanced FTMW instrument (6 - 20 GHz), and a millimeter-wave one (75 - 100 GHz, 140 - 214 GHz). Through the assignment of more than 6200 lines, accurate ground state spectroscopic constants (rotational, centrifugal distortion up to octics, and nuclear quadrupole hyperfine constants) have been derived from our measurements, with a plausible prediction of the weaker bands through calculations. Interstellar searches for this highly polar species can now be undertaken with confidence since the astronomically most interesting radio lines have either been measured or can be calculated to very high accuracy below 300 GHz.