Space-based atomic clocks provide unique conditions for testing General Relativity (GR) due to their stability in a low-disturbance environment and their exposure to significant variations in gravitational potential. Gravitational redshift (GRS), a direct consequence of the Einstein Equivalence Principle (EEP), causes clocks at different gravitational potentials to experience relative time dilation. Ground-to-space GRS experiments measure frequency shifts arising from differences in gravitational potential through signal exchange between ground and satellite clocks. While past experiments have relied on microwave links for time–frequency comparisons, optical time and frequency transfer has recently emerged as a promising alternative due to its immunity to ionospheric effects, reduced sensitivity to atmospheric delays, higher modulation bandwidth, and improved signal clarity. In this work, we investigate the GRS using ground-to-space observations from the Time Transfer by Laser Link (T2L2) experiment onboard the Jason-2 mission. Relative to the pioneering 1975 University of Maryland experiment, USA, the T2L2 mission achieves over an order-of-magnitude improvement in measurement precision, demonstrating the power of modern optical time transfer techniques. By comparing a ground-based hydrogen maser and a space-based ultra-stable quartz oscillator, with respective stabilities of and at 1000s, over 47 independent T2L2/Jason-2 passes (approximately 12 h total), we obtain a GRS deviation from GR of . These results demonstrate that optical time-transfer links can achieve high-precision tests of GR, underscoring their potential for future space-based optical timing missions.