The recent detection of SiN in the outer envelope of the IRC + carbon star has renewed the interest for the gas phase interstellar silicon chemistry. In this contribution, we present a theoretical study of the H2SiN+ molecular ion, the silicon hydrogenated counterpart of the previously studied SiNH2+. On many points, the differences relative to the SiNH2+ isomer have been found to be dramatic. As an example,the dipole moment is computed to be 3.8 D while being only 0.5 D in SiH2+. The radio, infrared and electronic signatures have been evaluated at a quantitative level. The rotational constants and vibrational frequencies have been determined using Moller-Plesset MPn (n=2,3,4), coupled cluster (CCSDT) and complete active space self-consistent field (CASSCF) methods for H2SiN+ and some of its isotopomers. These quantities have been corrected using a scaling procedure derived from previous studies on the HNSi, HSiN, HSiNH2, H2SiNH, and SiH2+ species in order to provide quantitative results. The failure of single-reference perturbation theories to predict a relevant infrared spectrum is discussed. Intense bands around 550, 950, and 2300 cm(-1) are predicted. The electronic spectrum has been obtained using a coupled multiconfiguration SCF-perturbation treatment (MC/P) : It is characterized by a large number of excited states, none of them having a strong transition moment. The lowest excited state is predicted to lie 0.54 eV above the ground state, but the first allowed transition having a nonnegligible oscillator strength has to be searched at 6.44 eV.