We present the first investigation of the Blue Straggler star (BSS) population in two isolated dwarf spheroidal galaxies of the Local Group, Cetus and Tucana. Deep HST/ACS photometry allowed us to identify samples of 940 and 1214 candidates, respectively. The analysis of the star formation histories of the two galaxies suggests that both host a population of BSSs. Specifically, if the BSS candidates are interpreted as young main sequence stars, they do not conform to their galaxy's age-metallicity relationship. The analysis of the luminosity function and the radial distributions support this conclusion, and suggest a non-collisional mechanism for the BSS formation, from the evolution of primordial binaries. This scenario is also supported by the results of new dynamical simulations presented here. Both galaxies coincide with the relationship between the BSS frequency and the absolute visual magnitude Mv found by Momany et al (2007). If this relationship is confirmed by larger sample, then it could be a valuable tool to discriminate between the presence of BSSs and galaxies hosting truly young populations. ; Comment: Accepted for publication on ApJ. 15 pages, 3 tables, 13 figures. A version with high resolution figure can be downloaded from http://rialto.ll.iac.es/proyecto/LCID/?p=publications