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We present a new calibration of the peak absolute magnitude of SNe Type 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 having SBF distance measurements. Applying a hierarchical Bayesian approach, we calibrate the SNe luminosity and extend it into the Hubble flow by using a sample of 96 SNe Ia in the redshift range $0.02 < z < 0.075$, extracted from the Combined Pantheon Sample. We estimate a value of $H_0 = 70.50 \pm 2.37(stat) \pm 3.38(sys)$ $\text{km}\ \text{s}^{-1}\ \text{Mpc}^{-1}$ (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, and consistent within the errors with the value obtained from SNe Type Ia calibrated with Cepheids and the one 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 the ones 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 SNe Ia progenitor properties. Sampling different host galaxy type, SBF offers a complementary approach to 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 LSST 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, and in the estimation of $H_0$.