Absorption spectra for Cn clusters (n = 2-8) are calculated using an adiabatic time-dependent density functional formalism within the local density approximation (TDLDA). We compare the calculated spectra with those computed using a simple local density approximation approach. It is readily observed that the TDLDA spectra display a significant blue shift with respect to the Kohn-Sham eigenvalue spectra. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations. We also obtain a significant threshold absorption, which can distinguish different ground states of the carbon clusters.