The article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a triangular domain into a double integral, and then directly determining formulas for the inner and outer integrals. The solution obtained is marked by high computational efficiency, high accuracy, and very simple implementation. The derived formula, in contrast to the currently available formulas, consists of quantities that have a clear and simple geometric interpretation, related to the geometry of the computational domain.