Cryptocurrencies, such as Bitcoin, are becoming increasingly popular, having been widely used as an exchange medium in areas such as financial transaction and asset transfer verification. However, there has been a lack of solutions that can support real-time price prediction to cope with high currency volatility, handle massive heterogeneous data volumes, including social media sentiments, while supporting fault tolerance and persistence in real time, and provide real-time adaptation of learning algorithms to cope with new price and sentiment data. In this paper we introduce KryptoOracle, a novel real-time and adaptive cryptocurrency price prediction platform based on Twitter sentiments. The integrative and modular platform is based on (i) a Spark-based architecture which handles the large volume of incoming data in a persistent and fault tolerant way; (ii) an approach that supports sentiment analysis which can respond to large amounts of natural language processing queries in real time; and (iii) a predictive method grounded on online learning in which a model adapts its weights to cope with new prices and sentiments. Besides providing an architectural design, the paper also describes the KryptoOracle platform implementation and experimental evaluation. Overall, the proposed platform can help accelerate decision-making, uncover new opportunities and provide more timely insights based on the available and ever-larger financial data volume and variety.