Sustainable and responsible investing has become a cornerstone of modern finance, promoting the integration of environmental, social, and governance (ESG) factors into investment decision-making. This approach enables investors to align financial performance with broader social and environmental objectives. However, ESG metrics are often affected by significant uncertainty due to differences in reporting standards, data availability, and subjective assessments. As a result, portfolio optimization must incorporate ESG considerations and address the reliability of the underlying data, leading to more complex and robust optimization models. This work proposes a robust version of the sparse mean-variance portfolio model that accounts for uncertainty in ESG measures through a box uncertainty set. We convert the uncertain problem into a bilevel optimization form, where the lower level problem represents the worst realization of the uncertain parameters. The resulting bi-level optimization problem is reformulated into a convex, non-smooth single-level problem by replacing the lower-level problem with its equivalent optimality conditions. The nonsmoothness arising from the l1 norm terms is addressed using a standard modeling trick, where each absolute value is replaced by the sum of two nonnegative variables representing its positive and negative parts. The resulting convex problem is then efficiently solved using second-order optimization methods. We compute numerical tests to real market data and compare the behaviour of the solutions obtained by the robust optimization algorithm and the solutions obtained by a certain one using nominal data.