High-precision spectrographs play a key role in exoplanet searches using the radial velocity technique. But at the accuracy level of 1 m.s-1, required for super-Earth characterization, stability of fiber-fed spectrograph performance is crucial considering variable observing conditions such as seeing, guiding and centering errors and, telescope vignetting. In fiber-fed spectrographs such as HARPS or SOPHIE, the fiber link scrambling properties are one of the main issues. Both the stability of the fiber near-field uniformity at the spectrograph entrance and of the far-field illumination on the echelle grating (pupil) are critical for high-precision radial velocity measurements due to the spectrograph geometrical field and aperture aberrations. We conducted tests on the SOPHIE spectrograph at the 1.93-m OHP telescope to measure the instrument sensitivity to the fiber link light feeding conditions: star decentering, telescope vignetting by the dome,and defocussing. To significantly improve on current precision, we designed a fiber link modification considering the spectrograph operational constraints. We have developed a new link which includes a piece of octagonal-section fiber, having good scrambling properties, lying inside the former circular-section fiber, and we tested the concept on a bench to characterize near-field and far-field scrambling properties. This modification has been implemented in spring 2011 on the SOPHIE spectrograph fibers and tested for the first time directly on the sky to demonstrate the gain compared to the previous fiber link. Scientific validation for exoplanet search and characterization has been conducted by observing standard stars. ; Comment: 12 pages, 9 figures, Proceedings of SPIE 2011