The deflection of starlight by the Sun is one of the classical tests of General Relativity (GR). In this work, we derive solar light deflection within Stiffness Field Cosmology (SFC), where gravity is not a fundamental interaction but an emergent refraction-like effect arising from spatial gradients of a vacuum stiffness field K(x). Starting from wavepacket propagation in an inhomogeneous elastic vacuum, we obtain the full deflection formula without invoking spacetime curvature. The predicted deflection angle matches the observed value α⊙ ≃ 1.75′′ at the solar limb. The achromatic nature of the effect is explained naturally, and conceptual differences with GR are clarified.