This paper examines the problem of optimizing the charging pattern of electric vehicles (EV) by taking real-time electricity grid carbon intensity into consideration. The objective of the proposed charging scheme is to minimize the carbon emissions contributed by EV charging events, while simultaneously satisfying constraints posed by EV user's charging schedules, charging station transformer limits, and battery physical constraints. Using real-world EV charging data and California electricity generation records, this paper shows that our carbon-aware real-time charging scheme saves an average of 3.81% of carbon emission while delivering satisfactory amount of energy. Furthermore, by using an adaptive balanced factor, we can reduce 26.00% of carbon emission on average while compromising 12.61% of total energy delivered.