Surface tension is defined as a tangential force acting per unit length at right angles to the either side of the imagined line drawn on the free liquid Surface of the liquid in the equilibrium state. read more
Surface tension [math]S = \dfrac{F}{l}[/math], where [math]F[/math] is force and [math]l[/math] is length of the surface. Force is a vector, and length here is a scalar. Therefore, surface tension is indeed a vector. read more