We have studied the effect of an external direct current (DC) electric field (similar to 1 kV/mm) on the rheological properties of colloidal suspensions consisting of aggregates of laponite particles in a silicone oil. Microscopy observations show that, under application of an electric field greater than a triggering electric field E-c similar to 0.6 kV/mm laponite aggregates assemble into chain- and/or columnlike structures in the oil. Without an applied electric field, the steady-state shear behavior of such suspensions is Newtonian-like. Under application of an electric field larger than Ec, it changes dramatically as a result of the changes in the microstructure: a significant yield stress is measured, and under continuous shear the fluid is shear-thinning. The theological properties, in particular the dynamic and static shear stress, were studied as a function of particle volume fraction for various strengths (including null) of the applied electric field. The flow curves at constant shear rate can be scaled with respect to both the particle fraction and electric field strength onto a master curve. This scaling is consistent with simple scaling arguments. The shape of the master curve accounts for the system's complexity; it approaches a standard power-law model at high Mason numbers. Both dynamic and static yield stresses are observed to depend on the particle fraction Phi and electric field E as Phi E-beta(alpha), with alpha similar to 1.85 and beta similar to 1 and 1.70 for the dynamic and static yield stresses, respectively. The yield stress was also determined as the critical stress at which there occurs a bifurcation in the theological behavior of suspensions that are submitted to a constant shear stress; a scaling law with alpha similar to 1.84 and beta similar to 1.70 was obtained. The effectiveness of the latter technique confirms that such electrorheological (ER) fluids can be studied in the framework of thixotropic fluids. The method is very reproducible; we suggest that it could be used routinely for studying ER fluids. The measured overall yield stress behavior of the suspensions may be explained in terms of standard conduction models for electrorheological systems. Interesting prospects include using such systems for guided self-assembly of clay nanoparticles.