We present the measurement of the energy spectrum of the boron flux in cosmic rays based on the data collected by the CALorimetric Electron Telescope (CALET) during 7.25 years of operation on the International Space Station. The energy spectrum is measured from 8.4 GeV/n to 3.8 TeV/n with an all calorimetric instrument with a total thickness corresponding to 1.3 nuclear interaction length and equipped with charge detectors capable of single element resolution. The observed boron flux shows a spectral hardening at the same transition energy E0 ~200 GeV/n of the carbon and oxygen spectra, though B flux has a different energy dependence with respect to C and O. Within the limitations of our data’s present statistical significance, the boron spectral index change is found to be slightly larger than that of carbon and oxygen, which are similar. A corresponding break in the energy dependence of the B/C and B/O flux ratios also supports the idea that the secondary cosmic rays exhibit a stronger hardening than primary ones. Moreover, interpreting our data with a Leaky Box model, we argue that the trend of the energy dependence of the B/C and B/O ratios in the TeV/n region could suggest a possible presence of a residual propagation path length, compatible with the hypothesis that a fraction of secondary B nuclei can be produced near the cosmic-ray source.