We present a novel tool BertRLFuzzer, a BERT and Reinforcement Learning (RL) based fuzzer aimed at finding security vulnerabilities for Web applications. BertRLFuzzer works as follows: given a set of seed inputs, the fuzzer performs grammar-adhering and attack-provoking mutation operations on them to generate candidate attack vectors. The key insight of BertRLFuzzer is the use of RL with a BERT model as an agent to guide the fuzzer to efficiently learn grammar-adhering and attack-provoking mutation operators. In order to establish the efficacy of BertRLFuzzer we compare it against a total of 13 black box and white box fuzzers over a benchmark of 9 victim websites with over 16K LOC. We observed a significant improvement, relative to the nearest competing tool in terms of time to first attack (54% less), new vulnerabilities found (17 new vulnerabilities), and attack rate (4.4% more attack vectors generated).