We have selected a complete sample of 80 flat-spectrum radio quasars (FSRQs) from the WMAP 7-yr catalog within the SDSS area, all with measured redshift, and have inspected their SEDs looking for evidence of an AGN torus emission. A SED fitting algorithm has found such evidence for seven objects and an uncertain indication for one more. These 8 FSRQs belong to the sub-sample of 55 sources showing the optical--ultraviolet bump interpreted as thermal emission from a standard accretion disc. Torus luminosities have been estimated for the eight objects whose torus was identified by the fitting algorithm. For the other 47 FSRQs in the sub-sample we have derived upper limits to the torus luminosity. Our analysis shows that the torus can show up clearly only under quite special conditions: low luminosity and preferentially low peak frequency of the beamed synchrotron emission from the jet; high torus luminosity, close to that of the accretion disc. This implies that the inferred ratios of torus to disc luminosity are biased high. The median value, considering upper limits as detections, is $L_{\rm torus}/L_{\rm disc}\sim 1$ while studies of radio quiet quasars yield average ratios $\langle L_{\rm torus}/L_{\rm disc}\rangle \simeq 1/3-1/2$. Our results are compatible with the FSRQ tori having the same properties of those of radio quiet quasars. At variance with Plotkin et al. (2012), who investigated a sample of optically selected BL Lacs, we find that the Wide-field Infrared Survey Explorer (WISE) infrared colors do not allow us to draw any conclusion on the presence or absence of tori associated with WMAP selected blazars. With the latter selection blazars of all types (FSRQs with and without evidence of torus, BL Lacs, blazars of unknown type) occupy the same region of the WISE color-color plane, and their region overlaps that of SDSS quasars with point-like morphology.