The growing prevalence and rapid evolution of offensive language in social media amplify the complexities of detection, particularly highlighting the challenges in identifying such content across diverse languages. This survey presents a systematic and comprehensive exploration of Cross-Lingual Transfer Learning (CLTL) techniques in offensive language detection in social media. Our study stands as the first holistic overview to focus exclusively on the cross-lingual scenario in this domain. We analyse 67 relevant papers and categorise these studies across various dimensions, including the characteristics of multilingual datasets used, the cross-lingual resources employed, and the specific CLTL strategies implemented. According to "what to transfer", we also summarise three main CLTL transfer approaches: instance, feature, and parameter transfer. Additionally, we shed light on the current challenges and future research opportunities in this field. Furthermore, we have made our survey resources available online, including two comprehensive tables that provide accessible references to the multilingual datasets and CLTL methods used in the reviewed literature.