Dirac spinors are central to relativistic quantum theory, but their incorporation into curved spacetime usually requires tetrads, local Lorentz frames, curved gamma matrices, and spin connections. This works successfully, but it leaves a conceptual asymmetry: general relativity is written in the language of geometric and tensorial objects, while spin-(\frac12) matter is introduced through an additional spinor representation layer. This paper develops a complementary geometric carrier formulation of Dirac spinors in curved spacetime. The construction begins with a Lorentzian metric (g_{\mu\nu}) and a physical direction of motion (u^\mu). From this motion anchor, the paper builds a rest-space projector (h^\mu{}\nu), a spin-axis selector (s^\mu), a transverse spin-plane projector (P_T{}^\mu{}\nu), and a phase-plane operator (I_{\mu\nu}). The key identity (I^2=-P_T) turns the transverse spin plane into a geometric complex structure and allows a half-angle rotor (U(\varphi)=\exp(\varphi I/2)), yielding the characteristic (2\pi) inversion and (4\pi) closure of spin-(\frac12) states. The carrier is then promoted to an even Clifford object (C\in Cl^+_{1,3}(M)), and the ordinary Dirac spinor is recovered as a local module readout (\psi_D=Cf) through an idempotent projection. Under module-preserving connection conditions, the carrier-native equation projects to the standard Dirac equation in curved spacetime. The construction also develops the associated bilinear structure and shows how the carrier satisfies the expected Fierz-compatible constraints of ordinary Dirac spinors. The purpose of this paper is not to replace the Dirac equation, eliminate spinoriality, quantize gravity, identify spin phase with electromagnetic (U(1)) gauge phase, or absorb chirality into a spin-axis selector. Instead, it provides a local and semiclassical geometric substrate for Dirac spinor structure while preserving the ordinary Dirac equation as the projected readout. The paper compares the construction with tetrad methods, vierbein-free and spin-base invariant approaches, Dirac-Hestenes and spacetime algebra formulations, Dirac–Kähler theory, and Fierz/Lounesto bilinear consistency. It also identifies two natural future stress tests of the carrier language: quantum wavepackets, where localization and momentum support limit the sharpness of the motion-anchored phase geometry, and horizon mode splitting, where different observer congruences may induce different carrier readouts near strong gravitational boundaries. The result is a motion-anchored geometric carrier interpretation of Dirac spinors in curved spacetime: the ordinary Dirac spinor is not discarded, but understood as the local Clifford-module readout of a geometric carrier whose spin-(\frac12) closure emerges from its transported transverse phase plane.