Cooperative networking is a promising technology to meet the rapidly growing demand of mobile data traffic. To stimulate effective and trustworthy user cooperation, we leverage the knowledge of the social tie structure among mobile users and develop a social trust based cooperative D2D relaying framework, which takes into account both physical distances and social distances among users. Based on (finite-horizon) optimal stopping theory, we derive the optimal social aware relay selection strategy, which strikes a balance between performance gain and relay probing cost. We further show that the optimal stopping policy for social aware relay selection exhibits a stage-dependent threshold structure that has a monotonically non-increasing property. Numerical results demonstrate that the proposed mechanism can yield significant throughput gain over the direct transmission scheme.