The recent emergence of reinforcement learning (RL) has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for inference in online learning are restricted to settings involving independently sampled observations, while inference methods in RL have so far been limited to the batch setting. The bootstrap is a flexible and efficient approach for statistical inference in online learning algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this article, we study the use of the online bootstrap method for inference in RL policy evaluation. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm across a range of real RL environments. Supplementary materials for this article are available online.