Phenomenological crystal plasticity models---thanks to their simple formulation---enable accurate and efficient prediction of micro-mechanical behavior with relatively few constitutive parameters. However, when multiple slip families are involved in plastic deformation, the deformation behavior becomes strongly coupled resulting in non-linear dependencies among slip family-specific constitutive parameters. This not only renders difficulties in the calibration process but also necessitates the procurement of additional data to address unequal contributions of the involved slip families. In the present work, a high-energy synchrotron diffraction experiment (HEXRD) was conducted in situ during mechanical testing of an additively manufactured and subsequently heat-treated Ti-6Al-4V titanium alloy. Lattice strain data from a number of planes was obtained from the in situ synchrotron diffraction experiment in addition to global stress-strain response during the uniaxial tensile test. The resulting data, lattice strain and tensile stress-strain curve, was used to calibrate the constitutive parameters of the hexagonal $\mathrm{\alpha}$-phase of the Ti-6Al-4V alloy. The parameters are discussed and compared against existing calibrated data from the literature.