We present an innovative impedance cytometer for the measurement of the cross-sectional position of single particles or cells flowing in a microchannel. As predicted by numerical simulations and experimentally validated, the proposed approach is applicable to particles/cells with either spherical or non-spherical shape. In particular, the optics-free high-throughput position detection of individual flowing red blood cells (RBCs) is demonstrated and applied to monitor RBCs hydrodynamic focusing under different sheath flow conditions. Moreover, the device provides multiparametric information useful for lab-on-a-chip applications, including particle inter-arrival times and velocity profile, as well as RBCs mean corpuscular volume, distribution width and electrical opacity.