Recent positron flux fraction measurements in cosmic-rays ( CR ) made by the AMS-02 detector confirm and extend the evidence on the existence of a new ( yet unknown ) source of high energy electrons and positrons . We test the gravitino dark matter of bilinear R-parity violating supersymmetric models as this electrons/positrons source . Being a long lived weak-interacting and spin 3/2 particle , it offers several particularities which makes it an attractive dark matter candidate . We compute the electron , positron and \gamma -ray fluxes produced by each gravitino decay channel as it would be detected at the Earth ’ s position . Combining the flux from the different decay modes we are able to reproduce AMS-02 measurements of the positron fraction , as well as the electron and positron fluxes , with a gravitino dark matter mass in the range 1 - 3 TeV and lifetime of \sim 1.0 - 0.7 \times 10 ^ { 26 } s. The high statistics measurement of electron and positron fluxes , and the flattening in the behaviour of the positron fraction recently found by AMS-02 allow us to determine that the preferred gravitino decaying mode by the fit is W ^ { \pm } \tau ^ { \mp } , unlike previous analyses . Then we study the viability of these scenarios through their implication in \gamma -ray observations . For this we use the Extragalactic \gamma -ray Background recently reported by the Fermi -LAT Collaboration and a state-of-the-art model of its known contributors . Based on the \gamma -ray analysis we exclude the gravitino parameter space which provides an acceptable explanation of the AMS-02 data . Therefore , we conclude that the gravitino of bilinear R-parity violating models is ruled out as the unique primary source of electrons and positrons needed to explain the rise in the positron fraction .