In these times of increasing cybersecurity threats, monitoring and analyzing cybersecurity events in a timely and effective way is the key to promote social media security. Twitter is one of the world's highly used social media networks where users can share their preferences, images, opinions, events, and so on. The Twitter platform can aggregate many cybersecurity-related events promptly and provide a source of information about cyber threats. Likewise, Machine Learning and Deep Learning Algorithms can play a critical role to help social media providers achieve a more accurate assessment of the cybersecurity threats. This research proposes a Deep Learning-based model to detect cybersecurity threats on Twitter. Cybersecurity threats are collated from the publicly available Twitter datasets to verify the model effectiveness and efficiency. This research can help Twitter developers to implement the proposed artificially intelligence (AI) driven model that improves the detection of cybersecurity threats with more accuracy in less time.