In this paper, we present ARAP-IRONY, a multi-dialectal Arabic irony corpus including 21,120 tweets covering 11 Arabic dialects, which we developed to enable the detection of irony in dialectal Arabic using machine learning. In fact, Arabic dialects exhibit important differences in pronunciation, grammar, and vocabulary so that it is quite hard from someone from the Gulf region for instance to understand someone from the Maghreb region. Our irony corpus is balanced in terms of gender and age groups. It includes 20 ironic and 20 non-ironic tweets from each of the 48 users per dialect region that are manually annotated. We conducted various machine learning experiments using this corpus to identify irony in Dialectal Arabic. The highest accuracy and F1-score of 70% was achieved using a Logistic Regression classifier with character n-gram feature extraction.