Technical Debt (TD) is a metaphor reflecting technical compromises that can yield short-term benefits but might hurt the long-term health of a software system. With the increasing amount of data generated when performing software development activities, an emergent research field has gained attention: applying Intelligent Techniques to solve Software Engineering problems. Intelligent Techniques were used to explore data for knowledge discovery, reasoning, learning, planning, perception, or supporting decision-making. Although these techniques can be promising, there is no structured understanding related to their application to support Technical Debt Management (TDM) activities. Within this context, this study aims to investigate to what extent the literature has proposed and evaluated solutions based on Intelligent Techniques to support TDM activities. To this end, we performed a Systematic Mapping Study (SMS) to investigate to what extent the literature has proposed and evaluated solutions based on Intelligent Techniques to support TDM activities. In total, 150 primary studies were identified and analyzed, dated from 2012 to 2021. The results indicated a growing interest in applying Intelligent Techniques to support TDM activities, the most used: Machine Learning and Reasoning under uncertainty. Intelligent Techniques aimed to assist mainly TDM activities related to identification, measurement, and monitoring. Design TD, Code TD, and Architectural TD are the TD types in the spotlight. Most studies were categorized at automation levels 1 and 2, meaning that existing approaches still require substantial human intervention. Symbolists and Analogizers are levels of explanation presented by most Intelligent Techniques, implying that these solutions conclude a general truth after considering a sufficient number of particular cases. Moreover, we also cataloged the empirical research types, contributions, and validation strategies described in primary studies. Based on our findings, we argue that there is still room to improve the use of Intelligent Techniques to support TDM activities. The open issues that emerged from this study can represent future opportunities for practitioners and researchers.