Context: Software traceability (ST) refers to capturing associations in various artifacts. A growing interest has been in applying machine learning (ML) techniques to ST. Objective: The purpose of this work is to present a comprehensive review of the state-of-the-art progress on the intersection of ML and ST. Method: A systematic mapping study (SMS) is conducted. A total of 965 citations are retrieved from 2013 to 2022, among which 37 studies are selected as primary studies. Result: 32 ML technologies and 9 enhancement strategies for generating trace links have been identified. Besides, 90 datasets and 16 measures have been summarized, which are applied to evaluate the efficacy of the ML-based tracing techniques. The overall reproducibility of these primary studies is at a medium level. Conclusion: We have found that ML is playing a positive role in improving the accuracy and efficiency of ST. However, there are still some challenges such as reproducibility. Hence, researchers are suggested to pay more attention to standardization to improve the reproducibility of studies.