Using a variational method, we show that an effective attractive force exists between two Gaussian laser beams in a plasma because of a mutual coupling from relativistic mass corrections. The effective force can be generalized to other nonlinearities. This force can cause two laser beams to spiral around each other with a rotation period that is proportional to the Rayleigh length. These orbits are stable if the ratio of the orbit diameter to the laser spot size d(0)/W(0)</=sqrt[2]. Three-dimensional particle-in-cell simulations are presented which confirm the mutual attraction.