We present a Generative Adversarial Network (GAN) based room impulse response generator (IR-GAN) for generating realistic synthetic room impulse responses (RIRs). IR-GAN extracts acoustic parameters from captured real-world RIRs and uses these parameters to generate new synthetic RIRs. We use these generated synthetic RIRs to improve far-field automatic speech recognition in new environments that are different from the ones used in training datasets. In particular, we augment the far-field speech training set by convolving our synthesized RIRs with a clean LibriSpeech dataset. We evaluate the quality of our synthetic RIRs on the real-world LibriSpeech test set created using real-world RIRs from the BUT ReverbDB and AIR datasets. Our IR-GAN reports up to an 8.95% lower error rate than Geometric Acoustic Simulator (GAS) in far-field speech recognition benchmarks. We further improve the performance when we combine our synthetic RIRs with synthetic impulse responses generated using GAS. This combination can reduce the word error rate by up to 14.3% in far-field speech recognition benchmarks.