Collapsing stars constitute the main black hole (BH) formation channel, and are occasionally associated with the launch of relativistic jets that power γ-ray bursts (GRBs). Thus, collapsars offer an opportunity to infer the natal (before spin-up/down by accretion) BH spin directly from observations. We show that once the BH saturates with a large-scale magnetic flux, the jet power is dictated by the BH spin and mass accretion rate. Core-collapse simulations by Halevi et al. and GRB observations favor stellar density profiles that yield an accretion rate of m ̇ ≈ 10 − 2 M ⊙ s − 1 , weakly dependent on time. This leaves the spin as the main factor that governs the jet power. By comparing the jet power to characteristic GRB luminosities, we find that the majority of BHs associated with jets are likely born slowly spinning with a dimensionless spin of a ≃ 0.2, or a ≃ 0.5 for wobbling jets, with the main uncertainty originating in the unknown γ-ray radiative efficiency. This result could be applied to the entire core-collapse BH population, unless an anticorrelation between the stellar magnetic field and angular momentum is present. In a companion paper, Jacquemin-Ide et al., we show that regardless of the natal spin, the extraction of BH rotational energy leads to spin-down to a ≲ 0.2, consistent with gravitational-wave observations. We verify our results by performing the first 3D general-relativistic magnetohydrodynamic simulations of collapsar jets with characteristic GRB energies, powered by slowly spinning BHs. We find that jets of typical GRB power struggle to escape from the star, providing the first numerical indication that many jets fail to generate a GRB.