Using millimeter-very long baseline interferometry (VLBI) observations of the BL Lac object S5 0716+714 from August 2008 to September 2013, we investigate variations in the core flux density and orientation of the sub-parsec scale jet i.e. position angle. The gamma-ray data obtained by the Fermi-LAT (Large Area Telescope) are used to investigate the high-energy flux variations over the same time period. For the first time in any blazar, we report a significant correlation between the gamma-ray flux variations and the position angle (PA) variations in the VLBI jet. The cross-correlation analysis also indicates a positive correlation such that the mm-VLBI core flux density variations are delayed with respect to the gamma-ray flux by 82$pm$32 days. This suggests that the high-energy emission is coming from a region located $geq$(3.8$pm$1.9) parsecs upstream of the mm-VLBI core (closer to the central black hole). These results imply that the observed inner jet morphology has a strong connection with the observed gamma-ray flares.
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