Recent advancements in natural language production provide an additional tool to manipulate public opinion on social media. Furthermore, advancements in language modelling have significantly strengthened the generative capabilities of deep neural models, empowering them with enhanced skills for content generation. Consequently, text-generative models have become increasingly powerful allowing the adversaries to use these remarkable abilities to boost social bots, allowing them to generate realistic deepfake posts and influence the discourse among the general public. To address this problem, the development of reliable and accurate deepfake social media message-detecting methods is important. Under this consideration, current research addresses the identification of machine-generated text on social networks like Twitter. In this study, a straightforward deep learning model in combination with word embeddings is employed for the classification of tweets as human-generated or bot-generated using a publicly available Tweepfake dataset. A conventional Convolutional Neural Network (CNN) architecture is devised, leveraging FastText word embeddings, to undertake the task of identifying deepfake tweets. To showcase the superior performance of the proposed method, this study employed several machine learning models as baseline methods for comparison. These baseline methods utilized various features, including Term Frequency, Term Frequency-Inverse Document Frequency, FastText, and FastText subword embeddings. Moreover, the performance of the proposed method is also compared against other deep learning models such as Long short-term memory (LSTM) and CNN-LSTM displaying the effectiveness and highlighting its advantages in accurately addressing the task at hand. Experimental results indicate that the streamlined design of the CNN architecture, coupled with the utilization of FastText embeddings, allowed for efficient and effective classification of the tweet data with a superior 93% accuracy.