Torsional moments pose significant risks to skewed bridges during earthquakes by inducing in-plane rotational motion of the superstructure, potentially leading to the unseating of girders from their supports. This research introduces a method to control the rotational motion of skewed bridges using nonlinear fluid viscous dampers (FVDs) positioned at the ends of the middle girders in each span. The proposed method relies on two key factors: first, leveraging the energy dissipation capabilities of these devices; second, utilizing their placement to establish an additional in-plane connection between the girder and the nearest vertical support (abutment or cap beam) to limit the in-plane rotational motion of the girders, thereby minimizing torsional moments. Six configurations for placing nonlinear FVDs were examined to identify the most effective alignment. The study was conducted on an existing 30° skewed bridge in Ismailia Governorate, Egypt, which features three simple spans with precast post-tensioned girders. Initial investigations focused on the behavior of the case study bridge with varying skew angles, and the results were compared with the proposed control cases. Detailed 3D finite element models were developed using CSI Bridge software, and nonlinear time history analyses were performed under the influence of bidirectional earthquake components. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) was employed to identify the optimal configuration for controlling rotational motion and torsional behavior in a skewed bridge. The results indicated that placing Fluid Viscous Dampers (FVDs) on opposite sides of the obtuse and acute angles; formed between the girders and vertical supports; provides the most effective setup, yielding performance comparable to that of a non-skewed bridge. The economic feasibility of this optimal configuration was evaluated by comparing its installation and maintenance costs with potential unseating damage scenarios over the bridge’s service life. The analysis showed that this approach not only enhances the seismic resilience of skewed bridges but also offers a cost-effective and environmental sustainability solution.