We study the magnetic behavior and in particular the spin magnetization of an interacting two-dimensional electron gas in an in-plane magnetic field. The ground-state energy of the system is constructed using the correlation energy based on the recent quantum Monte Carlo (QMC) simulations as a function of density, spin polarization, and applied magnetic field. The critical magnetic field to fully spin polarize the system is obtained as a function of the electron density. The spin polarization as a function of the applied field (less than the critical field) for various densities is calculated. When the QMC parametrization is employed, we find that the two-dimensional electron system undergoes a first-order phase transition to a ferromagnetic state in the regions 0 < r(s)< 7 and 20 < r(s)< 25, where r(s) is the usual density parameter. For 7 < r(s)< 20 our calculations indicate a second-order transition unlike approximate theories.