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The origin of the large-scale poloidal magnetic field required to power relativistic jets in collapsars remains uncertain. While such a field may be inherited during proto-neutron-star collapse, the efficiency of this process is unclear, motivating an in situ mechanism to generate poloidal fields out of the predominantly toroidal fields produced by stellar differential rotation. We present the first 3D general-relativistic magnetohydrodynamics collapsar simulations initialized with toroidal magnetic field profiles that closely follow those of precollapse stellar models. As the toroidal field in the disk becomes dynamically important, it seeds the dynamo, producing coherent poloidal magnetic loops that appear at <inline-formula> <mml:math><mml:mo>∼</mml:mo><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>100</mml:mn><mml:mo>)</mml:mo></mml:math> </inline-formula> gravitational radii and are then advected inward along paths that may deviate from the disk midplane. The resulting poloidal fields thread the black hole (BH) and launch highly variable, wobbling relativistic jets on timescales of order seconds, with the onset depending on the initial magnetic field and the plasma circularization radius. Although the jets are highly variable and misaligned with the BH spin axis, they sustain ≳10<SUP>50</SUP> erg s<SUP>−1</SUP>, comparable to that inferred for long gamma-ray bursts (LGRBs). We identify magnetic-flux inversions driven by the stochastic dynamo, leading to the formation of striped jets that could be imprinted in LGRB light curves. These results demonstrate that accretion-disk dynamos provide a robust pathway for jet production in collapsars across a broad range of progenitors.