This paper discusses the possibility of using a multi-objective optimization workflow to design Rogowski coil current sensor and optimize its performance. Seven geometrical parameters can be used as design variables to maximize objective functions such as sensor bandwidth and sensitivity. Based on the electrical lumped parameter model of the Rogowski coil, the sensor geometry is optimized combining a genetic algorithm (GA) in Matlab and a finite element (FE) electromagnetic model in Q3D Ansys. To validate the proposed design approach, a compact current sensor with very high bandwidth (up to 300 MHz) is designed, prototyped, tested, and compared with a suboptimal design (up to 100 MHz). Experimental results prove the validity and optimality of the sensor model used for the design.