Oleic acid is a simple molecule with an aliphatic chain and a carboxylic group whose ionization and, consequently, intermolecular interactions are strongly dependent on the solution pH. The titration curve of these molecules was already obtained using different experimental methods, which have shown the lipid bilayer assemblies to be stable between pH 7.0 and 9.0. In this work, we take advantage of our recent implementations of periodic boundary conditions in Poisson-Boltzmann calculations and ionic strength treatment in simulations of charged lipid bilayers, and we studied the ionization dependent behavior of an oleic acid bilayer using a new extension of the stochastic titration constant-pH MD method. With this new approach, we obtained titration curves that are in good agreement with the experimental data. Also, we were able to estimate the slope of the titration curve from charge fluctuations, which is an important test of thermodynamic consistency for the sampling in a constant-pH MD method. The simulations were performed for ionizations up to 50%, because an experimentally observed macroscopic transition to micelles occurs above this value. As previously seen for a binary mixture of a zwitterionic and an anionic lipid, we were able to reproduce experimental results with simulation boxes usually far from neutrality. This observation further supports the idea that a charged membrane strongly influences the ion distribution in its vicinity and that neutrality is achieved significantly far from the bilayer surface. The good results obtained with this extension of the stochastic titration constant-pH MD method strongly supports its usefulness to sample the coupling between configuration and protonation in these types of biophysical systems. This method stands now as a powerful tool to study more realistic lipid bilayers where pH can influence both the lipids and the solutes interacting with them.