Automatic Speech Recognition (ASR) based on Recurrent Neural Network Transducers (RNN-T) is gaining interest in the speech community. We investigate data selection and preparation choices aiming for improved robustness of RNN-T ASR to speech disfluencies with a focus on partial words. For evaluation we use clean data, data with disfluencies and a separate dataset with speech affected by stuttering. We show that after including a small amount of data with disfluencies in the training set the recognition accuracy on the tests with disfluencies and stuttering improves. Increasing the amount of training data with disfluencies gives additional gains without degradation on the clean data. We also show that replacing partial words with a dedicated token helps to get even better accuracy on utterances with disfluencies and stutter. The evaluation of our best model shows 22.5% and 16.4% relative WER reduction on those two evaluation sets.