Due to the presence of both Twitter-specific conventions and non-standard and dialectal language, Twitter presents a significant parsing challenge to current dependency parsing tools. We broaden English dependency parsing to handle social media English, particularly social media African-American English (AAE), by developing and annotating a new dataset of 500 tweets, 250 of which are in AAE, within the Universal Dependencies 2.0 framework. We describe our standards for handling Twitter- and AAE-specific features and evaluate a variety of cross-domain strategies for improving parsing with no, or very little, in-domain labeled data, including a new data synthesis approach. We analyze these methods' impact on performance disparities between AAE and Mainstream American English tweets, and assess parsing accuracy for specific AAE lexical and syntactic features. Our annotated data and a parsing model are available at: http://slanglab.cs.umass.edu/TwitterAAE/.