In this work we make use of a general relativistic method to estimate the mass-to-distance ratio M/D = 3.54−0.18+0.20 × 104 M⊙ Mpc−1 of the black hole hosted at the core of the active galactic nucleus of TXS 2226–184, along with its right ascension offset and the recession redshift (velocity) of the galaxy. Our statistical fit is based on the frequency shift of photons emitted by water masers and their orbital positions when circularly revolving around the black hole center within the accretion disk of the active galactic nucleus. By taking a previously reported distance to the galaxy into account, we compare the result of the black hole mass fit to an estimate based on a mass-luminosity correlation. We find that the black hole mass at the core of TXS 2226–184 obtained with the aid of the statistical fit using the general relativistic method, M = 3.67−0.18+0.20 × 106 M⊙, is approximately 0.6 times the black hole mass, MBH = 6.24−2.27+3.63 × 106 M⊙, which was computed with the mass–luminosity correlation.