The ability to combine symbols to generate language is a defining characteristic of human intelligence, particularly in the context of artistic story-telling through lyrics. We develop a method for synthesizing a rap verse based on the content of any text (e.g., a news article), or for augmenting pre-existing rap lyrics. Our method, called Rapformer, is based on training a Transformer-based denoising autoencoder to reconstruct rap lyrics from content words extracted from the lyrics, trying to preserve the essential meaning, while matching the target style. Rapformer features a novel BERT-based paraphrasing scheme for rhyme enhancement which increases the average rhyme density of output lyrics by 10%. Experimental results on three diverse input domains show that Rapformer is capable of generating technically fluent verses that offer a good trade-off between content preservation and style transfer. Furthermore, a Turing-test-like experiment reveals that Rapformer fools human lyrics experts 25% of the time.