Since aqueous acids release Hydrogen cations into the solution, will an electric current create Hydrogen gas? I was wondering that since acids dissociate in water to make a lot of  $\ce{H+}$ cations. Is it possible that introducing a supply of electrons via an electric current, would create $\ce{H2}$ gas?
Yes.  In fact the first electrolysis was done with acidified water.  Pure water is only slightly ionized and is a poor conductor.  Adding ions to water increases its conductivity and speeds up the electrolysis process.  So by adding a source of protons to pure water the following reaction will occur at the cathode $$\ce{2H+ (aq) + 2e^{-}-&gt;H2(g)}$$  Of course a parallel reaction will occur at the anode $$\ce{4OH- -&gt;2H2O + O2(g) + 4e-}$$ otherwise a current wouldn't flow and the electrolysis would not continue.