Trust is an important factor, particularly in viral/social advertising, and computing trust scores for individual users of a social network is crucial for several applications in the advertising research and practice. However, research on trust in the advertising field has been limited, and the application of computational trust to advertising research using big data is rare. Addressing the gap in the research literature, this study proposed and empirically tested a new social media analytics method, the Trust Scores in Social Media (TSM) algorithm, for measuring individual users' trust levels in a social network. TSM proposes the concept of negatively reinforced trust scores and introduces two complementary measures of trust, trustingness, and trustworthiness. Another unique and important element in the TSM algorithm is the incorporation of trust-decision involvement to adjust trust scores depending on the level of trust-decision involvement of different networks. Using small survey data and big data from social networks, this study demonstrated the effectiveness of the TSM algorithm. Various applications of the TSM algorithm to viral/social advertising research and practice are also discussed.