We present a new calibration of the peak absolute magnitude of Type Ia supernovae (SNe Ia) based on the surface brightness fluctuations (SBF) method, aimed at measuring the value of the Hubble constant. We build a sample of calibrating anchors consisting of 24 SNe hosted in galaxies that have SBF distance measurements. Applying a hierarchical Bayesian approach, we calibrate the SN Ia peak luminosity and extend the Hubble diagram into the Hubble flow by using a sample of 96 SNe Ia in the redshift range 0.02 <z <0.075, which was extracted from the Combined Pantheon Sample. We estimate a value of H-0 = 70.50 +/- 2.37 (stat.) +/- 3.38 (sys.) km s(-1) Mpc(-1) (i.e., 3.4% stat., 4.8% sys.), which is in agreement with the value obtained using the tip of the red giant branch calibration. It is also consistent, within errors, with the value obtained from SNe Ia calibrated with Cepheids or the value inferred from the analysis of the cosmic microwave background. We find that the SNe Ia distance moduli calibrated with SBF are on average larger by 0.07 mag than those calibrated with Cepheids. Our results point to possible differences among SNe in different types of galaxies, which could originate from different local environments and/or progenitor properties of SNe Ia. Sampling different host galaxy types, SBF offers a complementary approach to using Cepheids, which is important in addressing possible systematics. As the SBF method has the ability to reach larger distances than Cepheids, the impending entry of the Vera C. Rubin Observatory and JWST into operation will increase the number of SNe Ia hosted in galaxies where SBF distances can be measured, making SBF measurements attractive for improving the calibration of SNe Ia, as well as in the estimation of H-0.