SMS phishing, also known as "smishing", is a growing threat that tricks users into disclosing private information or clicking into URLs with malicious content through fraudulent mobile text messages. In recent past, we have also observed a rapid advancement of conversational generative AI chatbot services (e.g., OpenAI's ChatGPT, Google's BARD), which are powered by pre-trained large language models (LLMs). These AI chatbots certainly have a lot of utilities but it is not systematically understood how they can play a role in creating threats and attacks. In this paper, we propose AbuseGPT method to show how the existing generative AI-based chatbot services can be exploited by attackers in real world to create smishing texts and eventually lead to craftier smishing campaigns. To the best of our knowledge, there is no pre-existing work that evidently shows the impacts of these generative text-based models on creating SMS phishing. Thus, we believe this study is the first of its kind to shed light on this emerging cybersecurity threat. We have found strong empirical evidences to show that attackers can exploit ethical standards in the existing generative AI-based chatbot services by crafting prompt injection attacks to create newer smishing campaigns. We also discuss some future research directions and guidelines to protect the abuse of generative AI-based services and safeguard users from smishing attacks.