Twitter is a social media platform that is used to express sentiments about events, topics, individuals, and groups. Sentiments in Tweets can be classified as positive or negative expressions. However, in sentiment, there is an expression that is actually the opposite of what is mean to be, and this is called sarcasm. The existence of sarcasm in a Tweet is difficult to detect automatically by a system even by humans. In this research, we propose a weighting scheme based on inconsistency between sentimen of tweet contain in Indonesian and the usage of emoji. With the weighting scheme for the detection of sarcasm, it can be used to find out a sentiment about a event, topic, individual, group, or product's review. The proposed method is by calculating the distance between the textual feature polarity score obtained from the Convolutional Neural Network and the emoji polarity score in a Tweet. This method is used to find the boundary value between Tweets that contain sarcasm or not. The experimental results of the model developed, obtained f1-score 87.5%, precision 90.5% and recall 84.8%. By using the textual features and emoji models, it can detect sarcasm in a Tweet.