The fundamental building block of social influence is for one person to elicit a response in another. Researchers measuring a "response" in social media typically depend either on detailed models of human behavior or on platform-specific cues such as re-tweets, hash tags, URLs, or mentions. Most content on social networks is difficult to model because the modes and motivation of human expression are diverse and incompletely understood. We introduce content transfer, an information-theoretic measure with a predictive interpretation that directly quantifies the strength of the effect of one user's content on another's in a model-free way. Estimating this measure is made possible by combining recent advances in non-parametric entropy estimation with increasingly sophisticated tools for content representation. We demonstrate on Twitter data collected for thousands of users that content transfer is able to capture non-trivial, predictive relationships even for pairs of users not linked in the follower or mention graph. We suggest that this measure makes large quantities of previously under-utilized social media content accessible to rigorous statistical causal analysis.