Social Networking Sites have significant potential to reveal valuable explicit as well as implicit statistics and patterns when deep learning is applied to their raw and unstructured data. Tweets posted by the users on their timeline not only reflect their mindset, their likes and dislikes but could also be used to unveil significant amount of information about many psychological aspects and behavior that may be hard to study directly. This paper aims to predict the personality of the 100 real-time Twitter users conforming to personality traits in the BIG 5 model by extracting features from their tweets using ensemble of CNN (Convolutional Neural Network) and BiLSTM (Bidirectional Long Short Memory). The findings of our experiment shows that our model performs slightly better than previous baselines methods achieving an accuracy 75.134% on testing data. We have further hypothesized that unrestricted data available on Twitter may contain features that can be used to predict the personality of its user. It was concluded that personality of Twitter users in the real world is reflected in their online behaviour, reinforcing the premise that the nature of online interactions does not significantly differ from that of real-world interactions. Overall, the study provides a deep insight into the impact of social media data in providing predictive indicators of user behavior.