The aging population in Western countries has led to a rise in predementia conditions like Mild Cognitive Impairment (MCI). Social Assistive Robotics (SAR) interventions, among novel technological tools, offer a promising interdisciplinary approach to mitigate cognitive and social symptoms' progression in this clinical group. This systematic review aims to identify existing clinical protocols employing social robots for treating cognitive and social cognition skills in individuals with MCI. The review protocol adheres to the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. From six databases, we retrieved and analyzed 193 articles, of which 19 met the inclusion criteria, featuring samples diagnosed with MCI and subjected to cognitive and/or social interventions through SAR. The review encompasses both qualitative and quantitative studies, with a focus on assessing bias risk. Articles were categorized into four primary areas: study participants' samples, types of robots and programming used, assessment of cognitive abilities, and the nature of interventions (i.e., cognitive and and social cognition skills). While the findings highlight the potential benefits of using SAR for MCI interventions in both cognitive and social cognition domains, the studies primarily emphasized robot acceptability rather than intervention outcomes. Methodological limitations such as clinical heterogeneity, absence of control groups, and non-standardized assessments restrict the generalizability of these findings. This review underscores the promising role of Social Assistive Robotics in MCI interventions, emphasizing the importance of social cognition skills interventions and advocating for increased collaboration between clinicians and robotic researchers to overcome current limitations and enhance future outcomes.