Sarcasm primarily involves saying something but “meaning the opposite” or “meaning something completely different” in order to convey a particular tone or mood. In both the above cases, the “meaning” is reflected by the communicative intention of the speaker, known as dialogue acts. In this paper, we seek to investigate a novel phenomenon of analyzing sarcasm in the context of dialogue acts with the hypothesis that the latter helps to understand the former better. Toward this aim, we extend the multi-modal MUStARD dataset to enclose dialogue acts for each dialogue. To demonstrate the utility of our hypothesis, we develop a dialogue act-aided multi-modal transformer network for sarcasm identification (MM-SARDAC), leveraging interrelation between these tasks. In addition, we introduce an order-infused, multi-modal infusion mechanism into our proposed model, which allows for a more intuitive combined modality representation by selectively focusing on relevant modalities in an ordered manner. Extensive empirical results indicate that dialogue act-aided sarcasm identification achieved better performance compared to performing sarcasm identification alone. The dataset and code are available at https://github.com/mohit2b/MM-SARDAC.