The electron-impact ionization of atomic hydrogen with the electron's anomalous magnetic moment (AMM) effects are examined. The formulas for the laser-assisted relativistic triple differential cross section (TDCS) in the coplanar binary geometry developed earlier by Attaourti and Taj [Phys. Rev. A 69, 063411 (2004)] are used to check the consistency of our computations when the anomaly κ is taken to be zero. We show that the terms containing the AMM effects even in the first Born approximation has an important contribution, so it must be included in any reliable analysis. A full analytical calculation for the TDCS is presented.