Twitter is one of the most popular social platforms. It has changed the way of communication and information dissemination through its real-time messaging mechanism. Recently, it has been used by researchers and industries as a new source of data for various intelligent systems, such as tweet sentiment analysis and recommendation systems, which require high data quality. However, due to its flexibility and popularity, Twitter has become the main target for spamming activities such as phishing legitimate users or spreading malicious software, which introduces new security issues and waste resources. Therefore, researchers have developed various machine-learning algorithms to reveal Twitter spam. However, as spammers have become smarter and more crafty, the characteristics of the spam tweets are varying over time making these methods inefficient to detect new spammers tricks and strategies. In addition, some of the employed methods (e.g. blacklisting) or spammer features (e.g. graph-based features) are extremely time-consuming, which hinders the ability to detect spammer activities in real-time. In this paper, we introduce a framework to deal with the volatility of the spam contents and new spamming patterns, called the spam drift. The framework combines the strength of unsupervised machine learning approach, which learns from unlabeled tweets, to retrain a real-time supervised tweet-level spam detection model in a batch mode. A set of experiments on a large-scale data set show the effectiveness of the proposed online unsupervised method in adaptively discovers and learns the patterns of new spam activities and achieve stable recall values reaching more than 95%. Although the average spam precision of our method is around 60%, the high spam recall values show the ability of our proposed method in reducing spam drift problems compared to traditional machine learning algorithms.