A new implementation of pump-probe polarization spectroscopy is presented where the revivals of an impulsively excited rotational wavepacket are mapped onto a broad-band, chirped continuum pulse to measure a long temporal window without the need for delay scanning. Experimental measurements and a theoretical framework for spectral-temporal amplitude mapping polarization spectroscopy (STAMPS) as applied to impulsive rotational motion are presented. In this technique, a femtosecond laser pulse is used to prepare a rotational wavepacket in a gas-phase sample at room temperature. The rotational revivals of the wavepacket are then mapped onto a chirped continuum (400-800 nm) pulse created by laser filamentation in argon. Nearly single-shot time-resolved rotational spectra are recorded over a 65 ps time window. The transient birefringence spectra are simulated by including terms for polarization rotation of the probe as well as cross-phase modulation. Measurements and simulations are presented for the cylindrically symmetric N-2, O-2, and CO2 molecules. The long time window of the method allows measurement of rotational spectra for asymmetric top molecules, and here we present measurements for ethylene and methanol.