Cold dwell fatigue remains an important life-limiting factor in aircraft engine titanium alloys. Microstructure-level creep and stress accumulation during each loading cycle are controlled by strain rate sensitivity. Here, an integrated experimental and computational framework is used to link crystal-level slip properties to microstructure-sensitive cold dwell debit of a forged rotor graded Ti-6Al-4V alloy. Slip strengths and anisotropic strain rate sensitivities are extracted from micro-pillar compression tests for different slip systems, incorporated within α+β microstructurally-faithful polycrystal representations. Dwell and non-dwell cyclic loading in alloy Ti-6Al-4V are investigated for two differing microstructures, and the cycles to failure predicted based solely on the crystal c-axis tensile strength, and the dwell debit quantified. The dwell effect is predicted to diminish to zero below a peak applied stress of about 790 MPa in the alloy studied.