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We report results from the first Earth-space VLBI observations of the Galactic Center supermassive black hole, Sgr A*. These observations used the space telescope Spektr-R of the RadioAstron project together with a global network of 20 ground telescopes, observing at a wavelength of 1.35 cm. Spektr-R provided baselines up to 3.9 times the diameter of the Earth, corresponding to an angular resolution of approximately 55μas and a spatial resolution of 5.5R_Schat the source, whereR_Sch≡ 2GM/c²is the Schwarzschild radius of Sgr A*. Our short ground baseline measurements ( ≲ 80 Mλ) are consistent with an anisotropic Gaussian image, while our intermediate ground baseline measurements (100–250 Mλ) confirm the presence of persistent image substructure in Sgr A*. Both features are consistent with theoretical expectations for strong scattering in the ionized interstellar medium, which produces Gaussian scatter-broadening on short baselines and refractive substructure on long baselines. We do not detect interferometric fringes on any of the longer ground baselines or on any ground–space baselines. While space-VLBI offers a promising pathway to sharper angular resolution and the measurement of key gravitational signatures in black holes, such as their photon rings, our results demonstrate that space-VLBI studies of Sgr A* will require sensitive observations at submillimeter wavelengths.