Joint dependency parsing with disfluency detection is an important task in speech language processing. Recent methods show high performance for this task, although most authors make the unrealistic assumption that input texts are transcribed by human annotators. In real-world applications, the input text is typically the output of an automatic speech recognition (ASR) system, which implies that the text contains not only disfluency noises but also recognition errors from the ASR system. In this work, we propose a parsing method that handles both disfluency and ASR errors using an incremental shift-reduce algorithm with several novel features suited to ASR output texts. Because the gold dependency information is usually annotated only on transcribed texts, we also introduce an alignment-based method for transferring the gold dependency annotation to the ASR output texts to construct training data for our parser. We conducted an experiment on the Switchboard corpus and show that our method outperforms conventional methods in terms of dependency parsing and disfluency detection.