Abstract <p>We report a study of the features of the vortex supercurrent in a two-dimensional superconductor with two inverted electron bands and a Rashba spin‒orbit interaction between different orbitals. Using the tight-binding approximation and Bogoliubov‒de Gennes equations, an expression is derived for the supercurrent resulting from electron hopping between lattice sites with spin flips, which in turn are caused by the spin‒orbit interaction. It is shown that, at a significant spin‒orbit coupling intensity, this contribution to the total supercurrent can exceed the contribution from standard electron hopping processes in the lattice. Moreover, these contributions have different temperature dependences.</p>