Determining the detailed spin texture of topological surface states is important when one wants to apply topological insulators in spintronic devices. In principle, the in-plane spin component of the surface states can be measured by a method analogous to the so-called Meservey-Tedrow technique. Herein, it is suggested that the out-of-plane spin component can be determined by spin Hall effect tunneling spectroscopy. An analytical formula that allows to extract the out-of-plane spin component from spin Hall effect tunneling spectra is derived. The formula is tested using realistic tight-binding models of Bi2Se3 and Sb2Te3. It is demonstrated that the extracted out-of-plane spin polarization is in very good agreement with the actual out-of-plane spin polarization.